## [1] "!! high !! The experiment investigate the effects of two disturbance levels: low and high. To make it easier to interpet, we showcase only one of the two disturbance levels. In this document we showcase only the high disturbance)"

Design

Ecosystem size is a key factor driving biodiversity and ecosystem function. Larger ecosystems contain more species and can be hubs of dispersal and resource flows in networks of multiple ecosystems. However, whether and how ecosystem size and resource flows interact to affect biodiversity and ecosystem function has been largely overlooked. Here, we investigated how ecosystem size asymmetry affects biodiversity and function of two-ecosystem meta-ecosystems connected through flows of non-living resources. We conducted microcosm experiments, mimicking resource flows between ecosystems of different sizes, yet otherwise being identical. We found that meta-ecosystems with asymmetric ecosystem sizes had higher β-diversity but lower α-diversity and ecosystem function (total biomass) than their unconnected counterparts, while such an effect was not found for meta-ecosystems of identical ecosystem sizes. Our work demonstrates of how cross-ecosystem dynamics modulated by differences in ecosystem sizes affect biodiversity and function, with a direct implication for conservation and management of connected ecosystems.

Parameters

Parameters for R markdown and the general running of the code.

start_time = Sys.time()
knitr::opts_chunk$set(message = FALSE,
                      cache = FALSE,
                      autodep = FALSE)
recompute_lengthy_analyses = FALSE 

Parameters related to resource flows.

disturbance_levels = c("low", "high")
n_disturbance_levels = length(disturbance_levels)

resource_flow_days = c(5, 9, 13, 17, 21, 25)
first_resource_flow = resource_flow_days[1]

Parameters related to sampling.

total_frames = 125
volume_recorded_μl = 34.4
time_points = 0:7
time_points_without_t0 = 1:7
time_point_names = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
sampling_days = c(0, 4, 8, 12, 16, 20, 24, 28)
first_time_point = 0
last_time_point = length(sampling_days) - 1
n_time_points = last_time_point + 1
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2) #Videos taken for each time point for each culture. At t0 we took 12 videos of the large bottle from which we started the  cultures. Write why 2 at the end. 

videos_taken = data.frame(time_point = 0 : 7,
                          nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2))

n_videos_taken_t0 = nr_videos[1]

time_point_day = data.frame(time_point = first_time_point:last_time_point,
                            day = sampling_days,
                            video_replicates = nr_videos)

videos_to_take_off = data.frame(culture_ID = NA,
                                time_point = NA,
                                file = NA) %>%
                     add_row(culture_ID = 137-110, 
                             time_point = 7, 
                             file = 137) %>%
                     slice(-1)

n_cultures = 110
total_number_of_video_rows = sum(nr_videos * n_cultures)

Parameters related to protists.

protist_species = c("Ble", "Cep", "Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi", "Spi_te", "Tet")
protist_species_indiv_per_volume = paste0(protist_species, "_indiv_per_volume")
protist_species_indiv_per_ml = paste0(protist_species, "_indiv_per_ml")
protist_species_dominance = paste0(protist_species_indiv_per_ml, "_dominance")
protist_species_total = paste0(protist_species, "_tot_indiv")
n_protist_species = length(protist_species)
first_protist = protist_species[1]
last_protist = protist_species[n_protist_species]
species_IDD_with_13_threshold = c("Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi_te", "Tet")
species_IDD_with_13_threshold_indiv_per_volume = paste0(species_IDD_with_13_threshold, "_indiv_per_volume")
species_IDD_with_40_threshold = c("Ble", "Cep", "Spi")
species_IDD_with_40_threshold_indiv_per_volume = paste0(species_IDD_with_40_threshold, "_indiv_per_volume")

Parameters related to ecosystems.

ecosystems_to_take_off = 60 #Culture ID = 60 as it was spilled (small unconnected, high disturbance, system nr = 40)
ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)

columns_ecosystems = c("time_point",
                    "day",
                    "culture_ID",
                    "system_nr",
                    "disturbance",
                    "ecosystem_type",
                    "ecosystem_size",
                    "ecosystem_size_ml",
                    "size_connected_ecosystem",
                    "metaecosystem",
                    "metaecosystem_type")
columns_treatments = columns_ecosystems[!columns_ecosystems %in% c("system_nr", "culture_ID")]

variables_ecosystems = c("bioarea_mm2_per_ml",
                      "bioarea_tot_mm2",
                      "indiv_per_ml",
                      "indiv_tot",
                      "species_richness",
                      "shannon",
                      "simpson",
                      "inv_simpson",
                      "evenness_pielou",
                      "median_body_area_µm2",
                      paste0(protist_species, "_indiv_per_ml"),
                      paste0(protist_species, "_tot_indiv"),
                      paste0(protist_species_indiv_per_ml, "_dominance"))
baseline_columns = paste0("baseline_", variables_ecosystems)

ecosystem_types_ordered = c("Small connected to large",
                        "Small connected to small",
                        "Small unconnected",
                        "Medium connected to medium",
                        "Medium unconnected",
                        "Large connected to small",
                        "Large connected to large",
                        "Large unconnected")

treatments_and_controls = data.frame(treatment = c("Small connected to small",
                                                   "Small connected to large",
                                                   "Medium connected to medium",
                                                   "Large connected to large",
                                                   "Large connected to small"),
                                     control = c("Small unconnected",
                                                 "Small unconnected",
                                                 "Medium unconnected",
                                                 "Large unconnected",
                                                 "Large unconnected"))

n_treatments = length(unique(treatments_and_controls$treatment))
n_controls = length(unique(treatments_and_controls$control))
n_replicates = 5
n_ecosystem_types = 8

Parameters related to size classes.

n_size_classes = 12
columns_classes = c(columns_ecosystems,
                    "size_class_n",
                    "mean_class_area_µm2")

Parameters related to meta-ecosystems.

metaecosystems_to_take_off = ecosystems_info %>%
  filter(culture_ID %in% ecosystems_to_take_off) %>%
  pull(system_nr) %>%
  unique

system_nr_metaecosystems = ecosystems_info %>%
  filter(metaecosystem == "yes") %>%
  pull(system_nr) %>%
  unique

n_metaecosystems = length(system_nr_metaecosystems)

variables_metaecos = c(
  "total_metaecosystem_bioarea_mm2",
  "jaccard_index",
  "bray_curtis",
  "beta_spatial_turnover",
  "beta_nestedness",
  "beta_total",
  "metaecosystem_richness")

metaecosystem_types_ordered = c(
      "Small-Small meta-ecosystem",
      "Medium-Medium meta-ecosystem",
      "Medium-Medium unconnected",
      "Large-Large meta-ecosystem",
      "Small-Large meta-ecosystem",
      "Small-Large unconnected")

Name of the axes per response variable.

axis_names = data.frame(variable = NA,
                        axis_name= NA) %>%
  add_row(variable = "day", axis_name = "Time (day)") %>%
  add_row(variable = "ecosystem_size_ml", axis_name = "Patch size (ml)") %>%
  add_row(variable = "log_size_class", axis_name = "Log size (μm2)") %>%
  add_row(variable = "class_indiv_per_µl", axis_name = "Density (ind/ml)") %>%
  add_row(variable = "bioarea_mm2_per_ml", axis_name = "Biomass (mm2/ml)") %>%
  add_row(variable = "bioarea_mm2_per_ml_d", axis_name = "Bioamass ES") %>%
  add_row(variable = "bioarea_tot", axis_name = "Total Biomass (mm2)") %>%
  add_row(variable = "total_metaecosystem_bioarea_mm2", axis_name = "Total Biomass (mm2)") %>%
  add_row(variable = "species_richness", axis_name = "Species Richness") %>%
  add_row(variable = "species_richness_d", axis_name = "Species Richness ES") %>%
  add_row(variable = "mean_richness", axis_name = "Mean α-Diversity (Shannon)") %>%
  add_row(variable = "mean_shannon", axis_name = "Mean α-Diversity (Shannon)") %>%
  add_row(variable = "shannon", axis_name = "Biodiversity (Shannon)") %>%
  add_row(variable = "shannon_d", axis_name = "Biodiversity ES (Shannon ES)") %>%
  add_row(variable = "bray_curtis", axis_name = "β-Diversity (Bray-Curtis)") %>%
  add_row(variable = "beta_spatial_turnover", axis_name = "Turn over (Simpson pair-wise dissimilarity)") %>%
  add_row(variable = "beta_nestedness", axis_name = "Nestedness (nestedness-fraction of Sorensen)") %>%
  add_row(variable = "beta_total", axis_name = "Tot β-Diversity (Sorensen)") %>%
  add_row(variable = "metaecosystem_richness", axis_name = "γ-Diversity (Species Richness)") %>%
  add_row(variable = "indiv_per_ml", axis_name = "Abundance (ind/ml)") %>%
  add_row(variable = "indiv_per_ml_d", axis_name = "Abundance ES") %>%
  add_row(variable = "median_body_area_µm2", axis_name = "Median Body Size (µm²)") %>%
  add_row(variable = "median_body_area_µm2_d", axis_name = "Median Body Size ES") %>%
  add_row(variable = "Ble_indiv_per_ml", axis_name = "Ble Density (ind/ml)") %>% 
  add_row(variable = "Cep_indiv_per_ml", axis_name = "Cep Density (ind/ml)") %>%
  add_row(variable = "Col_indiv_per_ml", axis_name = "Col Density (ind/ml)") %>%
  add_row(variable = "Eug_indiv_per_ml", axis_name = "Eug Density (ind/ml)") %>%
  add_row(variable = "Eup_indiv_per_ml", axis_name = "Eup Density (ind/ml)") %>%
  add_row(variable = "Lox_indiv_per_ml", axis_name = "Lox Density (ind/ml)") %>%
  add_row(variable = "Pau_indiv_per_ml", axis_name = "Pau Density (ind/ml)") %>%
  add_row(variable = "Pca_indiv_per_ml", axis_name = "Pca Density (ind/ml)") %>%
  add_row(variable = "Spi_indiv_per_ml", axis_name = "Spi Density (ind/ml)") %>%
  add_row(variable = "Spi_te_indiv_per_ml", axis_name = "Spi te Density (ind/ml)") %>%
  add_row(variable = "Tet_indiv_per_ml", axis_name = "Tet Density (ind/ml)") %>%
  add_row(variable = "auto_hetero_ratio", axis_name = "Photosynthetisers-Heterotrops Ratio") %>%
  add_row(variable = "Ble_indiv_per_ml_d", axis_name = "Ble Density ES") %>%
  add_row(variable = "Cep_indiv_per_ml_d", axis_name = "Cep Density ES") %>%
  add_row(variable = "Col_indiv_per_ml_d", axis_name = "Col Density ES") %>%
  add_row(variable = "Eug_indiv_per_ml_d", axis_name = "Eug Density ES") %>%
  add_row(variable = "Eup_indiv_per_ml_d", axis_name = "Eup Density ES") %>%
  add_row(variable = "Lox_indiv_per_ml_d", axis_name = "Lox Density ES") %>%
  add_row(variable = "Pau_indiv_per_ml_d", axis_name = "Pau Density ES") %>%
  add_row(variable = "Pca_indiv_per_ml_d", axis_name = "Pca Density ES") %>%
  add_row(variable = "Spi_indiv_per_ml_d", axis_name = "Spi Density ES") %>%
  add_row(variable = "Spi_te_indiv_per_ml_d", axis_name = "Spi te Density ES") %>%
  add_row(variable = "Tet_indiv_per_ml_d", axis_name = "Tet Density ES") %>%
  add_row(variable = "Ble_indiv_per_ml_dominance", axis_name = "Ble Dominance (%)") %>%
  add_row(variable = "Cep_indiv_per_ml_dominance", axis_name = "Cep Dominance (%)") %>%
  add_row(variable = "Col_indiv_per_ml_dominance", axis_name = "Col Dominance (%)") %>%
  add_row(variable = "Eug_indiv_per_ml_dominance", axis_name = "Eug Dominance (%)") %>%
  add_row(variable = "Eup_indiv_per_ml_dominance", axis_name = "Eup Dominance (%)") %>%
  add_row(variable = "Lox_indiv_per_ml_dominance", axis_name = "Lox Dominance (%)") %>%
  add_row(variable = "Pau_indiv_per_ml_dominance", axis_name = "Pau Dominance (%)") %>%
  add_row(variable = "Pca_indiv_per_ml_dominance", axis_name = "Pca Dominance (%)") %>%
  add_row(variable = "Spi_indiv_per_ml_dominance", axis_name = "Spi Dominance (%)") %>%
  add_row(variable = "Spi_te_indiv_per_ml_dominance", axis_name = "Spi te Dominance (%)") %>%
  add_row(variable = "Tet_indiv_per_ml_dominance", axis_name = "Tet Dominance (%)") %>%
  add_row(variable = "Ble_indiv_per_ml_dominance_d", axis_name = "Ble Dominance ES") %>%
  add_row(variable = "Cep_indiv_per_ml_dominance_d", axis_name = "Cep Dominance ES") %>%
  add_row(variable = "Col_indiv_per_ml_dominance_d", axis_name = "Col Dominance ES") %>%
  add_row(variable = "Eug_indiv_per_ml_dominance_d", axis_name = "Eug Dominance ES") %>%
  add_row(variable = "Eup_indiv_per_ml_dominance_d", axis_name = "Eup Dominance ES") %>%
  add_row(variable = "Lox_indiv_per_ml_dominance_d", axis_name = "Lox Dominance ES") %>%
  add_row(variable = "Pau_indiv_per_ml_dominance_d", axis_name = "Pau Dominance ES") %>%
  add_row(variable = "Pca_indiv_per_ml_dominance_d", axis_name = "Pca Dominance ES") %>%
  add_row(variable = "Sp_indiv_per_mli_dominance_d", axis_name = "Spi Dominance ES") %>%
  add_row(variable = "Spi_te_indiv_per_ml_dominance_d", axis_name = "Spi te Dominance ES") %>%
  add_row(variable = "Tet_indiv_per_ml_dominance_d", axis_name = "Tet Dominance ES") %>%
  add_row(variable = "dominance", axis_name = "Dominance (%)") %>%
  add_row(variable = "log_abundance", axis_name = "Log Abundance + 1 (ind/mm²)") %>%
  add_row(variable = "abundance_hedges_d", axis_name = "Density ES") %>%
  add_row(variable = "beta_diversity_from_unconnected", axis_name = "Divergence from unconnected") %>%
  add_row(variable = "beta_diversity_from_previous_time", axis_name = "Temporal Divergence") %>%
  add_row(variable = "beta_diversity_from_previous_time_d", axis_name = "Temporal Divergence ES") %>%
  add_row(variable = "evenness_pielou", axis_name = "Evenness") %>%
  add_row(variable = "evenness_pielou_d", axis_name = "Evenness ES") %>%
  slice(-1)

Colour and line type per ecosystem/meta-ecosystem type.

parameters_treatments = data.frame(treatment = NA,
                                colour = NA,
                                linetype = NA) %>%
  add_row(treatment = "Small connected to large", colour = "#feb24c", linetype = "solid") %>%
  add_row(treatment = "Small connected to small", colour = "#feb24c", linetype = "dashed") %>%
  add_row(treatment = "Small unconnected", colour = "#bdbdbd", linetype = "solid") %>% 
  add_row(treatment = "Large connected to small", colour = "#3182bd", linetype = "solid") %>%
  add_row(treatment = "Large connected to large", colour = "#3182bd", linetype = "dashed") %>%
  add_row(treatment = "Large unconnected", colour = "#000000", linetype = "solid") %>%
  add_row(treatment = "Medium connected to medium", colour = "#de2d26", linetype = "solid") %>%
  add_row(treatment = "Medium unconnected", colour = "#737373", linetype = "solid") %>%
  add_row(treatment = "Small-Large meta-ecosystem", colour = "#762a83", linetype = "solid") %>%
  add_row(treatment = "Small-Large unconnected", colour = "#762a83", linetype = "dashed") %>%
  add_row(treatment = "Medium-Medium meta-ecosystem", colour = "#1b7837", linetype = "solid") %>%
  add_row(treatment = "Medium-Medium unconnected", colour = "#1b7837", linetype = "dashed") %>%
  add_row(treatment = "Large-Large meta-ecosystem", colour = "#67000d", linetype = "solid") %>%
  add_row(treatment = "Small-Small meta-ecosystem", colour = "#fc9272", linetype = "solid") %>%
  slice(-1)

Parameters for plotting.

figures_height_rmd_output = 7

legend_position = "top"
legend_width_cm = 2
size_legend = 12
size_x_axis = 13
size_y_axis = size_x_axis
boxplot_width = 2
dodging = 0.5 
width_errorbar = 0.2
dodging_error_bar = 0.5

treatment_lines_linewidth = 1
treatment_points_size = 2.5

resource_flow_line_type = "solid"
resource_flow_line_colour = "#d9d9d9"
resource_flow_line_width = 0.3

zero_line_colour = "grey"
zero_line_line_type = "dotted"
zero_line_line_width = 0.5
zero_line_ES_line_type = "dotted"
zero_line_ES_colour = "grey"
zero_line_ES_line_width = 1

ggarrange_margin_top = 0
ggarrange_margin_bottom = 0
ggarrange_margin_left = 0
ggarrange_margin_right = 0

paper_width = 17.3
paper_height = 20
paper_units = "cm"
paper_res = 600
paper_y_axis_size = 9
paper_labels_size = 9

presentation_figure_size = 15
presentation_figure_width = 30
presentation_figure_height = 22
presentation_legend_size = 20
presentation_x_axis_size = 22
presentation_y_axis_size = presentation_x_axis_size
presentation_axes_size = 12
presentation_treatment_points_size = 5
presentation_treatment_linewidth = 2
presentation_figure_units = "cm"
presentation_figure_res = 600

grey_background_xmin = -Inf
grey_background_xmax = 7.5
grey_background_ymin = -Inf
grey_background_ymax = Inf
grey_background_fill = "#f0f0f0"
grey_background_alpha = 0.03
grey_background_color = "transparent"

Parameters for modelling.

first_time_point_model = 2 #Time point 2 is the first after disturbance
last_time_point_model = last_time_point

optimizer_input = 'Nelder_Mead'
method_input = ''

compar_ex = "The full and fixed models are compared to the null model."

results_table = data.frame(Response = as.character(NA),
                           Levels = as.character(NA),
                           ΔAIC_full = NA,
                           p_full = NA,
                           ΔR2_full = NA,
                           ΔAIC_fix = NA,
                           p_fix = NA,
                           ΔR2_fix = NA) %>%
  slice(-1)

Data

Ecosystems information (ecosystems_info)

We start by importing the information about the 110 ecosystems of the experiment.

ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)

Individuals (ds_individuals)

In this dataset (ds_individuals) each row represents an individual at a time point.

# Import the individual data of t0. We considered cultures to be all the same at the beginning (t0). Because of this reason, we filmed only the bottles from which cultures were assembled. Because we want to plot also t0 for the different treatments, we want to assign the video of bottles to all cultures at t0.

ds_individuals_t0_not_elongated = read.csv(here("2_data", 
                                                "individuals_13_threshold", 
                                                "t0.csv")) %>%
  mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
         day = 0,
         file =  as.numeric(str_extract(file, "\\d+")),
         video_replicate = file) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         id,
         N_frames,
         mean_area)

ds_individuals_t0_elongated = ds_individuals_t0_not_elongated %>%
  map_dfr(.x = 1 : nrow(ecosystems_info),
          .f = ~ ds_individuals_t0_not_elongated) %>% 
  arrange(id) %>% #Id refers to an individual
  mutate(culture_ID = rep(1 : nrow(ecosystems_info),
                          times = nrow(ds_individuals_t0_not_elongated))) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         culture_ID,
         id,
         N_frames,
         mean_area)

expect_equal(nrow(ds_individuals_t0_not_elongated) * nrow(ecosystems_info),
             nrow(ds_individuals_t0_elongated))
#Import t1-t4

ds_individuals_t1_to_t4 = NULL
  
for (time_point_i in time_points_without_t0) {
  
  ds_individuals_t1_to_t4[[time_point_i]] = read.csv(here("2_data", 
                                                          "individuals_13_threshold", 
                                                          paste0("t", 
                                                                 time_point_i, 
                                                                 ".csv"))) %>%
    mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
           day = time_point_day$day[time_point_day$time_point == time_point_i],
           file =  as.numeric(str_extract(file, "\\d+")),
           video_replicate = ceiling(file/n_cultures)) #Until 110 video replicate = 1, then 2
  }

ds_individuals_t1_to_t4 = ds_individuals_t1_to_t4 %>%
  bind_rows() %>%
  select(time_point,
         day,
         video_replicate,
         file,
         culture_ID,
         id,
         N_frames,
         mean_area)
# Bind t0 with t1-t4

ds_individuals = rbind(ds_individuals_t0_elongated,
                       ds_individuals_t1_to_t4) %>%
  left_join(ecosystems_info,
            by = "culture_ID") 
# Rename and select columns

ds_individuals = ds_individuals %>% 
  rename(ecosystem_size = patch_size,
         ecosystem_size_volume = patch_size_volume) %>%
  select(
    disturbance,
    disturbance_volume,
    time_point,
    day,
    video_replicate,
    culture_ID,
    system_nr,
    file,
    eco_metaeco_type,
    ecosystem_size,
    ecosystem_size_volume,
    metaecosystem,
    metaecosystem_type,
    mean_area,
    N_frames
  ) %>%
  rename(ecosystem_size_ml = ecosystem_size_volume,
         ecosystem_type = eco_metaeco_type,
         body_area_µm2 = mean_area)
# Rename and reorder levels

ds_individuals <- ds_individuals %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "S" ~ "Small unconnected",
                                ecosystem_type == "M" ~ "Medium unconnected",
                                ecosystem_type == "L" ~ "Large unconnected",
                                ecosystem_type == "S (S_S)" ~ "Small connected to small",
                                ecosystem_type == "S (S_L)" ~ "Small connected to large",
                                ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
                                ecosystem_type == "L (S_L)" ~ "Large connected to small",
                                ecosystem_type == "L (L_L)" ~ "Large connected to large",
                                TRUE ~ ecosystem_type),
         ecosystem_type = factor(ecosystem_type,
                             levels = ecosystem_types_ordered))

ds_individuals <- ds_individuals %>%
  mutate(ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
                                ecosystem_size == "M" ~ "Medium",
                                ecosystem_size == "L" ~ "Large",
                                TRUE ~ ecosystem_type),
         ecosystem_size = factor(ecosystem_size,
                             levels = "Small", 
                                      "Medium", 
                                      "Large"))

ds_individuals <- ds_individuals %>%
  mutate(size_connected_ecosystem = case_when(ecosystem_type == "Small connected to small" ~ "Small",
                                          ecosystem_type == "Small connected to large" ~ "Large",
                                          ecosystem_type == "Medium connected to medium" ~ "Medium",
                                          ecosystem_type == "Large connected to large" ~ "Large",
                                          ecosystem_type == "Large connected to small" ~ "Small",
                                          TRUE ~ NA_character_))
# Take off problematic videos

ds_individuals_before_taking_off_videos = ds_individuals

ds_individuals = ds_individuals %>%
  filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))

diff = setdiff(ds_individuals_before_taking_off_videos, ds_individuals)

expect_equal(nrow(videos_to_take_off),
             nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))
# Take off problematic cultures 

ds_individuals_before_taking_off_cultures = ds_individuals

ds_individuals = ds_individuals %>%
  filter(!culture_ID %in% ecosystems_to_take_off)

expect_equal(setdiff(ds_individuals_before_taking_off_cultures, 
                     ds_individuals) %>% 
               pull(culture_ID) %>% 
               unique(),
             ecosystems_to_take_off)

Patches (ds_ecosystems)

In this dataset (ds_ecosystems) each row represents a ecosystem at a time point. I use the data from the 40 threshold analysis for Ble, Cep, Spi and the data from the 13 threshold analysis for all the other protists (Col, Eup, Lox, Pau, Pca, Spi te, Tet).

# Import & bind t0 datasets.

ds_ecosystems_t0 = read.csv(here("2_data", 
                              "ecosystems_13_threshold", 
                              "t0.csv")) %>%
  mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
         day = 0,
         video_replicate = file) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         bioarea_per_volume,
         indiv_per_volume)

species_ID_13_threshold_t0 = read.csv(here("2_data", 
                                           "species_ID_13_threshold", 
                                           paste0("t0.csv"))) %>%
  rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
  select(file,
         all_of(species_IDD_with_13_threshold_indiv_per_volume))

species_ID_40_threshold_t0 = read.csv(here("2_data", 
                                           "species_ID_40_threshold", 
                                           paste0("t0.csv"))) %>%
  rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
  select(file,
         all_of(species_IDD_with_40_threshold_indiv_per_volume))

ds_ecosystems_t0 = ds_ecosystems_t0 %>%
  left_join(species_ID_13_threshold_t0,
            by = "file") %>%
  left_join(species_ID_40_threshold_t0,
            by = "file") %>%
  mutate(file =  as.numeric(str_extract(file, "\\d+")))
# Elongate t0 dataset.

ds_ecosystems_t0_elongated <- list()

for (video_i in 1 : n_videos_taken_t0) {
  
  single_video = ds_ecosystems_t0 %>%
    filter(file == video_i)
  
  ds_ecosystems_t0_elongated[[video_i]] = ecosystems_info %>%
    mutate(
      time_point = 0,
      day = 0,
      file = single_video$file,
      video_replicate = single_video$video_replicate,
      bioarea_per_volume = single_video$bioarea_per_volume,
      indiv_per_volume = single_video$indiv_per_volume,
      Ble_indiv_per_volume = single_video$Ble_indiv_per_volume,
      Cep_indiv_per_volume = single_video$Cep_indiv_per_volume,
      Col_indiv_per_volume = single_video$Col_indiv_per_volume,
      Eug_indiv_per_volume = single_video$Eug_indiv_per_volume,
      Eup_indiv_per_volume = single_video$Eup_indiv_per_volume,
      Lox_indiv_per_volume = single_video$Lox_indiv_per_volume,
      Pau_indiv_per_volume = single_video$Pau_indiv_per_volume,
      Pca_indiv_per_volume = single_video$Pca_indiv_per_volume,
      Spi_indiv_per_volume = single_video$Spi_indiv_per_volume,
      Spi_te_indiv_per_volume = single_video$Spi_te_indiv_per_volume,
      Tet_indiv_per_volume = single_video$Tet_indiv_per_volume)
}

ds_ecosystems_t0_elongated = ds_ecosystems_t0_elongated %>%
  bind_rows()
# Clean the columns of t0

ds_ecosystems_t0 = ds_ecosystems_t0_elongated %>%
  select(
    file,
    time_point,
    day,
    culture_ID,
    video_replicate,
    bioarea_per_volume,
    indiv_per_volume,
    all_of(protist_species_indiv_per_volume))

expect_equal(nrow(ds_ecosystems_t0), sum(n_videos_taken_t0 * n_cultures))
# Import and bind t1-t4

ds_ecosystems_t1_to_t4 = NULL

for (time_point_i in time_points_without_t0) {
  
  species_ID_13_threshold = read.csv(here("2_data", 
                                          "species_ID_13_threshold", 
                                          paste0("t", time_point_i, ".csv"))) %>%
    rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
    select(file,
           all_of(species_IDD_with_13_threshold_indiv_per_volume))
  
  
  species_ID_40_threshold = read.csv(here("2_data", 
                                          "species_ID_40_threshold", 
                                          paste0("t", time_point_i, ".csv"))) %>%
    rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
    select(file,
           all_of(species_IDD_with_40_threshold_indiv_per_volume))
  
  
  ds_ecosystems_t1_to_t4[[time_point_i]] = read.csv(here("2_data", 
                                                      "ecosystems_13_threshold", 
                                                      paste0("t", time_point_i, ".csv"))) %>%
    arrange(file) %>%
    mutate(video_replicate = rep(1 : time_point_day$video_replicates[time_point_i+1],
                                 each = n_cultures),
           day = time_point_day$day[time_point_day$time_point == time_point_i]) %>%
    select(
      file,
      time_point,
      day,
      video_replicate,
      file,
      culture_ID,
      bioarea_per_volume,
      indiv_per_volume)
  
  ds_ecosystems_t1_to_t4[[time_point_i]] = ds_ecosystems_t1_to_t4[[time_point_i]] %>%
    left_join(species_ID_13_threshold,
                by = "file") %>%
    left_join(species_ID_40_threshold,
                by = "file")
    
}

ds_ecosystems_t1_to_t4 = ds_ecosystems_t1_to_t4 %>%
  bind_rows()
# Bind t0 with t1-t4

ds_ecosystems = rbind(ds_ecosystems_t0,
                   ds_ecosystems_t1_to_t4) %>%
             left_join(ecosystems_info,
                       by = "culture_ID") 
    
expect_equal(nrow(ds_ecosystems),
             sum(sum(time_point_day$video_replicates) * n_cultures))
# Reorder and rename columns

ds_ecosystems = ds_ecosystems %>%
  rename(ecosystem_size = patch_size,
         ecosystem_size_ml = patch_size_volume) %>%
  select(
    file,
    time_point,
    day,
    disturbance,
    culture_ID,
    system_nr,
    eco_metaeco_type,
    ecosystem_size,
    ecosystem_size_ml,
    metaecosystem,
    metaecosystem_type,
    video_replicate,
    bioarea_per_volume,
    indiv_per_volume,
    all_of(protist_species_indiv_per_volume)
  ) %>%
  rename(ecosystem_type = eco_metaeco_type,
         bioarea_µm2_per_μL = bioarea_per_volume) %>%
  rename_all( ~ gsub("volume", "μL", .))
# Rename and reorder levels

ds_ecosystems <- ds_ecosystems %>%
  mutate(
    ecosystem_type = case_when(
      ecosystem_type == "S" ~ "Small unconnected",
      ecosystem_type == "M" ~ "Medium unconnected",
      ecosystem_type == "L" ~ "Large unconnected",
      ecosystem_type == "S (S_S)" ~ "Small connected to small",
      ecosystem_type == "S (S_L)" ~ "Small connected to large",
      ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
      ecosystem_type == "L (S_L)" ~ "Large connected to small",
      ecosystem_type == "L (L_L)" ~ "Large connected to large",
      TRUE ~ ecosystem_type
    ),
    ecosystem_type = factor(x = ecosystem_type,
                        levels = ecosystem_types_ordered),
    ecosystem_size = case_when(
      ecosystem_size == "S" ~ "Small",
      ecosystem_size == "M" ~ "Medium",
      ecosystem_size == "L" ~ "Large",
      TRUE ~ ecosystem_size
    ),
    metaecosystem_type = case_when(
      metaecosystem_type == "S_S" ~ "Small-Small meta-ecosystem",
      metaecosystem_type == "M_M" ~ "Medium-Medium meta-ecosystem",
      metaecosystem_type == "L_L" ~ "Large-Large meta-ecosystem",
      metaecosystem_type == "S_L" ~ "Small-Large meta-ecosystem",
      TRUE ~ metaecosystem_type
    ),
    size_connected_ecosystem = case_when(
      ecosystem_type == "Small connected to small" ~ "Small",
      ecosystem_type == "Small connected to large" ~ "Large",
      ecosystem_type == "Medium connected to medium" ~ "Medium",
      ecosystem_type == "Large connected to large" ~ "Large",
      ecosystem_type == "Large connected to small" ~ "Small",
      TRUE ~ NA_character_
      ),
    time_point =  as.numeric(str_extract(time_point, "\\d+")),
    file =  as.numeric(str_extract(file, "\\d+")),
  )
# Change units of measurments to ml

ds_ecosystems = ds_ecosystems %>%
  mutate(bioarea_µm2_per_ml = bioarea_µm2_per_μL * 10^3,
         bioarea_mm2_per_ml = bioarea_µm2_per_ml * 10^(-6),
         Ble_indiv_per_ml = Ble_indiv_per_μL * 10^3,
         Cep_indiv_per_ml = Cep_indiv_per_μL * 10^3,
         Col_indiv_per_ml = Col_indiv_per_μL * 10^3,
         Eug_indiv_per_ml = Eug_indiv_per_μL * 10^3,
         Eup_indiv_per_ml = Eup_indiv_per_μL * 10^3,
         Lox_indiv_per_ml = Lox_indiv_per_μL * 10^3,
         Pau_indiv_per_ml = Pau_indiv_per_μL * 10^3,
         Pca_indiv_per_ml = Pca_indiv_per_μL * 10^3,
         Spi_indiv_per_ml = Spi_indiv_per_μL * 10^3,
         Spi_te_indiv_per_ml = Spi_te_indiv_per_μL * 10^3,
         Tet_indiv_per_ml = Tet_indiv_per_μL * 10^3)
# Take off problematic videos

ds_ecosystems_before_taking_off_videos = ds_ecosystems

ds_ecosystems = ds_ecosystems %>%
  filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))

diff = setdiff(ds_ecosystems_before_taking_off_videos, ds_ecosystems)

expect_equal(nrow(videos_to_take_off),
             nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))
# Take off problematic cultures 

ds_ecosystems_before_taking_off_cultures = ds_ecosystems

ds_ecosystems = ds_ecosystems %>%
  filter(!culture_ID %in% ecosystems_to_take_off)

expect_equal(setdiff(ds_ecosystems_before_taking_off_cultures, 
                     ds_ecosystems) %>% 
               pull(culture_ID) %>% 
               unique(),
             ecosystems_to_take_off)
# Average videos

ds_ecosystems = ds_ecosystems %>%
  group_by(across(all_of(columns_ecosystems))) %>%
  summarise(across(contains("_per_ml"), mean),
            across(contains("_tot"), mean)) %>%
  ungroup()

expect_equal(nrow(ds_ecosystems), 
             (n_cultures - length(ecosystems_to_take_off)) * length(time_points))
# Add connection and individuals

ds_ecosystems = ds_ecosystems %>%
  mutate(indiv_per_ml = !!rlang::parse_expr(paste(protist_species_indiv_per_ml, 
                                                  collapse = " + ")))

ds_ecosystems = ds_ecosystems %>%
  mutate(connection = ifelse(str_detect(ecosystem_type, "unconnected"), 
                             "unconnected", 
                             "connected"),
         connection = factor(x = connection,
                        levels = c("unconnected", "connected")))
# Calculate total response variable for the whole ecosystem

ds_ecosystems = ds_ecosystems %>%
  mutate(bioarea_tot_mm2 = bioarea_mm2_per_ml * ecosystem_size_ml,
         indiv_tot = indiv_per_ml * ecosystem_size_ml,
         Ble_tot_indiv = Ble_indiv_per_ml * ecosystem_size_ml,
         Cep_tot_indiv = Cep_indiv_per_ml * ecosystem_size_ml,
         Col_tot_indiv = Col_indiv_per_ml * ecosystem_size_ml,
         Eug_tot_indiv = Eug_indiv_per_ml * ecosystem_size_ml,
         Eup_tot_indiv = Eup_indiv_per_ml * ecosystem_size_ml,
         Lox_tot_indiv = Lox_indiv_per_ml * ecosystem_size_ml,
         Pau_tot_indiv = Pau_indiv_per_ml * ecosystem_size_ml,
         Pca_tot_indiv = Pca_indiv_per_ml * ecosystem_size_ml,
         Spi_tot_indiv = Spi_indiv_per_ml * ecosystem_size_ml,
         Spi_te_tot_indiv = Spi_te_indiv_per_ml * ecosystem_size_ml,
         Tet_tot_indiv = Tet_indiv_per_ml * ecosystem_size_ml)
# Calculate species dominance

ds_ecosystems = ds_ecosystems %>%
  mutate(across(.cols = all_of(protist_species_indiv_per_ml), 
                .fns = list(dominance = ~ (. / indiv_per_ml) * 100), 
                .names = "{col}_dominance"))

expect_equal(unique(ds_ecosystems$Ble_indiv_per_ml_dominance[ds_ecosystems$indiv_per_ml == 0]), NaN)

if (FALSE %in% unique((ds_ecosystems$Ble_indiv_per_ml/ds_ecosystems$indiv_per_ml) *100 == ds_ecosystems$Ble_indiv_per_ml_dominance)) stop()
# Calculate alpha diversity (Shannon, Simpson, Inverse Simpson, Evenness)

n_rows_ds_ecosystems_before_calculating_alpha = nrow(ds_ecosystems)

ds_ecosystems = calculate.alpha.diversity()

expect_equal(max(ds_ecosystems$species_richness), 
             length(protist_species))

expect_equal(nrow(ds_ecosystems),
             n_rows_ds_ecosystems_before_calculating_alpha)
# Calculate median body size

n_rows_ds_ecosystems_before_median_size = nrow(ds_ecosystems)

ds_median_body_size = ds_individuals %>%
  group_by(time_point,
           culture_ID,
           file) %>%
  summarise(median_body_area_µm2 = median(body_area_µm2)) %>%
  group_by(time_point,
           culture_ID) %>%
  summarise(median_body_area_µm2 = mean(median_body_area_µm2))

expect_true(nrow(ds_median_body_size) <= nrow(ds_ecosystems)) #Ds median body size could be less because some cultures might be crashed and not have any individual.

ds_ecosystems_before_full_join = ds_ecosystems

ds_ecosystems = full_join(ds_ecosystems, ds_median_body_size)

expect_equal(nrow(ds_ecosystems), 
             n_rows_ds_ecosystems_before_median_size)
# Calculate auto/heterotrophic ratio

ds_ecosystems = ds_ecosystems %>%
  mutate(auto_hetero_ratio = (Eug_indiv_per_ml + Eup_indiv_per_ml) / 
                             (Ble_indiv_per_ml + 
                              Cep_indiv_per_ml + 
                              Col_indiv_per_ml + 
                              Lox_indiv_per_ml + 
                              Pau_indiv_per_ml + 
                              Pca_indiv_per_ml +
                              Spi_indiv_per_ml + 
                              Spi_te_indiv_per_ml +
                              Tet_indiv_per_ml))

Patch effect sizes (ds_ecosystems_effect_size)

In this dataset (ds_ecosystems_effect_size) each row represents a treatment at a time point. It contains the effect size of the connection of a ecosystem (connected vs unconnected).

# Calculate the mean & sd of response variables for each treatment/control at each time point

ds_ecosystems_effect_size = NULL
variable_nr = 0

for (variable_i in variables_ecosystems) {
  
  variable_nr = variable_nr + 1
  
  ds_ecosystems_effect_size[[variable_nr]] = ds_ecosystems %>%
    filter(time_point >= 1,
           !is.na(!!sym(variable_i))) %>%
    group_by(across(all_of(columns_ecosystems[columns_ecosystems != "culture_ID" & 
                                           columns_ecosystems != "system_nr"]))) %>%
    summarise(across(all_of(variable_i),
                     list(mean = mean,
                          sd = sd)),
              sample_size = n()) %>%
    rename_with( ~ paste0(variable_i, "_sample_size"),
                 matches("sample_size"))
  
}

ds_ecosystems_effect_size <- reduce(ds_ecosystems_effect_size,
                                 full_join,
                                 by = columns_ecosystems[columns_ecosystems != "culture_ID" &
                                                        columns_ecosystems != "system_nr"])

expect_equal(nrow(ds_ecosystems_effect_size),
             n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)
# Calculate the effect size (Hedge's d) for each treatment at each time point
  
  for (variable_i in variables_ecosystems) {
    ds_ecosystems_effect_size <- ds_ecosystems_effect_size %>%
      mutate(
        !!paste0(variable_i, "_d") := NA,
        !!paste0(variable_i, "_d_upper") := NA,
        !!paste0(variable_i, "_d_lower") := NA
      )
  }
  
  row_n = 0
  for (treatment_input in treatments_and_controls$treatment) {
    for (time_point_input in time_points) {
      row_n = row_n + 1
      
      control_input = treatments_and_controls$control[
        treatments_and_controls$treatment == treatment_input
        ]
      
      treatment_row = ds_ecosystems_effect_size %>%
        filter(ecosystem_type == treatment_input,
               time_point == time_point_input)
      
      control_row = ds_ecosystems_effect_size %>%
        filter(ecosystem_type == control_input,
               time_point == time_point_input)
      
      for (response_variable in variables_ecosystems) {
        
        hedges_d = calculate.hedges_d(
          treatment_row[[paste0(response_variable, "_mean")]],
          treatment_row[[paste0(response_variable, "_sd")]],
          treatment_row[[paste0(response_variable, "_sample_size")]],
          control_row[[paste0(response_variable, "_mean")]],
          control_row[[paste0(response_variable, "_sd")]],
          control_row[[paste0(response_variable, "_sample_size")]]
        )
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_input &
          ds_ecosystems_effect_size$time_point == time_point_input] =
          hedges_d$d
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d_upper")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_input &
          ds_ecosystems_effect_size$time_point == time_point_input] =
          hedges_d$upper_CI
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d_lower")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_input &
          ds_ecosystems_effect_size$time_point == time_point_input] =
          hedges_d$lower_CI
        
      }
    }
  }

expect_equal(nrow(ds_ecosystems_effect_size),
             n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)

Meta-ecosystems (ds_metaecosystems)

In this dataset (ds_metaecosystems) each row represents a meta-ecosystem or a two-ecosystem unconnected system at a time point.

#Find combinations of ecosystems in unconnected two-ecosystem systems.

ID_unconnected_S_low = ds_ecosystems %>%
  filter(ecosystem_type == "Small unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_M_low = ds_ecosystems %>%
  filter(ecosystem_type == "Medium unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_L_low = ds_ecosystems %>%
  filter(ecosystem_type == "Large unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_S_high = ds_ecosystems %>%
  filter(ecosystem_type == "Small unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_M_high = ds_ecosystems %>%
  filter(ecosystem_type == "Medium unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_L_high = ds_ecosystems %>%
  filter(ecosystem_type == "Large unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()
# Find combinations of ecosystems to create different two-ecosystem unconnected systems

combinations_S_and_L_low = crossing(ID_unconnected_S_low,
                                    ID_unconnected_L_low) %>%
                            mutate(disturbance = "low",
                                   metaecosystem_type = "Small-Large unconnected") %>%
                            rename(ID_first_ecosystem = ID_unconnected_S_low,
                                   ID_second_ecosystem = ID_unconnected_L_low) %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)

combinations_S_and_L_high = crossing(ID_unconnected_S_high,
                                     ID_unconnected_L_high) %>%
                            mutate(disturbance = "high",
                                   metaecosystem_type = "Small-Large unconnected") %>%
                            rename(ID_first_ecosystem = ID_unconnected_S_high,
                                   ID_second_ecosystem = ID_unconnected_L_high) %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)

combinations_M_and_M_low = combinat::combn(ID_unconnected_M_low,
                                   m = 2) %>%
                            t() %>%
                            as.data.frame() %>%
                            rename(ID_first_ecosystem = V1,
                                   ID_second_ecosystem = V2) %>%
                            mutate(disturbance = "low",
                                   metaecosystem_type = "Medium-Medium unconnected") %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)


combinations_M_and_M_high = combinat::combn(ID_unconnected_M_high,
                                   m = 2) %>%
                            t() %>%
                            as.data.frame() %>%
                            rename(ID_first_ecosystem = V1,
                                   ID_second_ecosystem = V2) %>%
                            mutate(disturbance = "high",
                                   metaecosystem_type = "Medium-Medium unconnected") %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)
# Bind combinations

combinations_unconnected_systems = rbind(combinations_S_and_L_low,
                                      combinations_S_and_L_high,
                                      combinations_M_and_M_low,
                                      combinations_M_and_M_high) %>%
  mutate(system_nr = 1001:(1000 + nrow(.))) %>%
  select(system_nr,
         disturbance,
         metaecosystem_type,
         ID_first_ecosystem,
         ID_second_ecosystem)
# Find combinations of ecosystems that were connected to form meta-ecosystems.

combinations_metaecos = ds_ecosystems %>%
  filter(time_point == 0,
         metaecosystem == "yes") %>%
  select(system_nr,
         disturbance,
         metaecosystem_type,
         culture_ID) %>%
  group_by(system_nr,
           disturbance,
           metaecosystem_type) %>%
  summarise(ID_first_ecosystem = (mean(culture_ID) - 0.5),
            ID_second_ecosystem = (mean(culture_ID) + 0.5)) %>%
  as.data.frame()
#Bind unconnected two-ecosystem systems and meta-ecosystems

ecosystem_combinations = rbind(combinations_unconnected_systems,
                           combinations_metaecos) %>%
  mutate(connection = ifelse(metaecosystem_type %in% c("Medium-Medium unconnected",
                                                       "Small-Large unconnected"),
                             yes = "unconnected",
                             no = "connected"),
         ecosystems_combined = paste0(ID_first_ecosystem, "|", ID_second_ecosystem))

n_ecosystems_combinations = nrow(ecosystem_combinations)
#Create sets for SL unconnected, where in each set a small and a large ecosystems are paired differently. To do so, I keep the small ecosystems on the same order and perform permutations on large ecosystems.

SL_unconnected_sys_sets <- vector("list",
                               length(disturbance_levels))

for (disturbance_i in 1:length(disturbance_levels)) {
  
  ID_small_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Small unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  ID_large_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Large unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  #Force small and large ecosystems vectors to have the same length
  length_difference <- length(ID_small_ecosystems) - length(ID_large_ecosystems)
  if (length_difference > 0) {
    
    ID_large_ecosystems = c(ID_large_ecosystems,
                       rep("Patch taken off",
                           times = abs(length(ID_small_ecosystems) - 
                                       length(ID_large_ecosystems))))
    
    } else if (length_difference < 0) {
      
    ID_small_ecosystems = c(ID_small_ecosystems,
                         rep("Patch taken off",
                             times = abs(length(ID_large_ecosystems) - 
                                         length(ID_small_ecosystems))))
    }

  # Create dataframe
  permutations_large = permn(ID_large_ecosystems)
  
  SL_unconnected_sys_sets[[disturbance_i]] = data.frame(
    disturbance = disturbance_levels[disturbance_i],
    metaecosystem_type = "Small-Large unconnected",
    connection = "unconnected",
    ID_first_ecosystem = rep(ID_small_ecosystems, times = length(permutations_large)),
    ID_second_ecosystem = unlist(permutations_large),
    set = rep(1 : length(permutations_large), each = length(ID_small_ecosystems)))
  
  expect_equal(nrow(SL_unconnected_sys_sets[[disturbance_i]]),
               length(ID_small_ecosystems) * length(permutations_large))
  
  SL_unconnected_sys_sets[[disturbance_i]] = SL_unconnected_sys_sets[[disturbance_i]] %>%
    filter(!ID_first_ecosystem == "Patch taken off",
           !ID_second_ecosystem == "Patch taken off") %>%
    mutate(ID_first_ecosystem = as.double(ID_first_ecosystem),
           ID_second_ecosystem = as.double(ID_second_ecosystem)) %>%
    full_join(ecosystem_combinations %>%
                filter(disturbance == disturbance_levels[disturbance_i], 
                       metaecosystem_type == "Small-Large unconnected")) #Add system_nr & ecosystems_combined

}

SL_unconnected_sys_sets_before_binding = SL_unconnected_sys_sets
SL_unconnected_sys_sets = SL_unconnected_sys_sets %>%
  bind_rows()
expect_equal(nrow(SL_unconnected_sys_sets),
             nrow(SL_unconnected_sys_sets_before_binding[[1]]) + nrow(SL_unconnected_sys_sets_before_binding[[2]]))

expect_equal(length(SL_unconnected_sys_sets %>% 
                      pull(system_nr) %>% 
                      unique()),
             length(ecosystem_combinations %>%
                      filter(metaecosystem_type == "Small-Large unconnected") %>%
                      pull(system_nr) %>%
                      unique()))
#WORK HERE

#Create sets for MM unconnected, where in each set two medium ecosystems small are paired differently. To do so, I ... 

#Initialise MM_unconnected_sets. Assign 10^4 rows to each matrix so that we have enough rows not to run out of them when we try to assign values to them. Assign 4 columns which will include culture_ID of the first system, second culture_ID of the fist system, culture_ID of the second system, and second culture_ID of the second system.  
MM_unconnected_sets = NULL
for(disturbance_i in 1:length(disturbance_levels)){
  
  MM_unconnected_sets[[disturbance_i]] <- matrix(nrow = 10 ^ 4, 
                                              ncol = 4)
  
}

for (disturbance_i in 1:length(disturbance_levels)) {
  
  ID_medium_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Medium unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  MM_unconnected_systems = combn(ID_medium_ecosystems, 
                              2) %>%
    t()
  
  matrix_row = 0
  for (first_system_i in 1:nrow(MM_unconnected_systems)) {
    
    #Find culture IDs of the first system (what's the first system?)
    first_system = MM_unconnected_systems[first_system_i, ]
    
    for (second_system_i in 1:nrow(MM_unconnected_systems)) {
      
      #Find culture IDs of the second system (what's the second system?)
      second_system = MM_unconnected_systems[second_system_i, ]
      
      shared_elements_among_systems = intersect(first_system,
                                                second_system)
      
      if (length(shared_elements_among_systems) == 0) {
        
        matrix_row = matrix_row + 1
        
        #Make first and second system into a set
        MM_unconnected_sets[[disturbance_i]][matrix_row,] = c(first_system,
                                                            second_system)
        
        print(MM_unconnected_sets[[disturbance_i]][matrix_row,])
        
      }
    }
  }
  
  #Tidy the dataset with all the ecosystem combinations
  MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets[[disturbance_i]] %>%
    as.data.frame() %>%
    drop_na()
  
  expect_equal(MM_unconnected_sets[[disturbance_i]] %>% 
                 filter(V1 == V2 | V1 == V3 | V1 == V4 | V2 == V3 | V2 == V4 | V3 == V4) %>% 
                 nrow(),
               0)
  
  #Reorder the dataset with all the ecosystem combinations
  MM_unconnected_sets_reordered = data.frame(ID_first_ecosystem = NA,
                                          ID_second_ecosystem = NA,
                                          set = NA)
  
  for (set_input in 1:nrow(MM_unconnected_sets[[disturbance_i]])) {
    MM_unconnected_sets_reordered = MM_unconnected_sets_reordered %>%
      add_row(
        ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 1],
        ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 2],
        set = set_input
      ) %>%
      add_row(
        ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 3],
        ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 4],
        set = set_input
      )
  }
  
  #Add to a list
  MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets_reordered %>%
    drop_na() %>%
    mutate(
      disturbance = disturbance_levels[disturbance_i],
      metaecosystem_type = "Medium-Medium unconnected",
      connection = "unconnected"
    )
  
  #Add system nr
  ID_combinations_MM_unconnected = ecosystem_combinations %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           metaecosystem_type == "Medium-Medium unconnected")
  
  MM_unconnected_sets[[disturbance_i]] = full_join(MM_unconnected_sets[[disturbance_i]],
                                                     ID_combinations_MM_unconnected)
  
}
## [1] 6 7 8 9
## [1]  6  7  8 10
## [1]  6  7  9 10
## [1] 6 8 7 9
## [1]  6  8  7 10
## [1]  6  8  9 10
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## [1]  6  9  7 10
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## [1]  6 10  7  8
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## [1] 7 8 6 9
## [1]  7  8  6 10
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## [1]  7  9  6 10
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## [1]  7 10  6  8
## [1]  7 10  6  9
## [1]  7 10  8  9
## [1] 8 9 6 7
## [1]  8  9  6 10
## [1]  8  9  7 10
## [1]  8 10  6  7
## [1]  8 10  6  9
## [1]  8 10  7  9
## [1]  9 10  6  7
## [1]  9 10  6  8
## [1]  9 10  7  8
## [1] 61 62 63 64
## [1] 61 62 63 65
## [1] 61 62 64 65
## [1] 61 63 62 64
## [1] 61 63 62 65
## [1] 61 63 64 65
## [1] 61 64 62 63
## [1] 61 64 62 65
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## [1] 61 65 62 64
## [1] 61 65 63 64
## [1] 62 63 61 64
## [1] 62 63 61 65
## [1] 62 63 64 65
## [1] 62 64 61 63
## [1] 62 64 61 65
## [1] 62 64 63 65
## [1] 62 65 61 63
## [1] 62 65 61 64
## [1] 62 65 63 64
## [1] 63 64 61 62
## [1] 63 64 61 65
## [1] 63 64 62 65
## [1] 63 65 61 62
## [1] 63 65 61 64
## [1] 63 65 62 64
## [1] 64 65 61 62
## [1] 64 65 61 63
## [1] 64 65 62 63
#Bind all sets of MM unconnected
MM_unconnected_sets = MM_unconnected_sets %>%
  bind_rows()
expect_equal(length(MM_unconnected_sets %>%
                      pull(system_nr) %>%
                      unique()),
             length(ecosystem_combinations %>%
                      filter(metaecosystem_type == "Medium-Medium unconnected") %>%
                      pull(system_nr) %>%
                      unique()))
#Bind SL and MM unconnected systems

unconnected_combinations_sets = rbind(SL_unconnected_sys_sets, 
                                   MM_unconnected_sets) %>%
  select(disturbance,
         metaecosystem_type,
         connection,
         set,
         system_nr,
         ID_first_ecosystem,
         ID_second_ecosystem)
  • Each row is a meta-ecosystem.

  • It contains also “fake” meta-ecosystems which I created from unconnected ecosystems (metaecosystem type = Small-Large unconnected & metaecosystem type = Medium-Medium unconnected).

  • Warning appear after the following code, as:

  1. alpha diversity is computed for a culture that is totally crashed, so it has not meaning.
  2. beta diversity is computed between a culture that is still alive and one that is totally crashed. Because one of the cultures is totally crashed, the Bray-Curtis index is 1.
#Compute meta-ecosystems  for each time point 

ds_metaecosystems = NULL
row_n = 0
for (combination in 1:n_ecosystems_combinations) {
  for (time_point_input in time_points) {
    row_n = row_n + 1
    
    current_day = sampling_days[time_point_input + 1]
    current_system_nr = ecosystem_combinations[combination, ]$system_nr
    current_combination = ecosystem_combinations[combination, ]$ecosystems_combined
    current_disturbance = ecosystem_combinations[combination, ]$disturbance
    current_metaeco_type = ecosystem_combinations[combination, ]$metaecosystem_type
    current_IDs = c(ecosystem_combinations[combination, ]$ID_first_ecosystem,
                    ecosystem_combinations[combination, ]$ID_second_ecosystem)
    
    if (current_system_nr %in% metaecosystems_to_take_off)
      next
    
    if (current_IDs[1] == current_IDs[2])
      next
    
    species_vector_two_ecosystems = ds_ecosystems %>%
      filter(time_point == time_point_input,
             culture_ID %in% current_IDs) %>%
      ungroup() %>%
      select(all_of(protist_species_indiv_per_ml))
    
    absence_presence_two_ecosystems <-
      ifelse(species_vector_two_ecosystems > 0, 1, 0)
    
    #Alpha diversity: Shannon (mean between the two ecosystems)
    shannon_ecosystem_1 = diversity(species_vector_two_ecosystems[1, ], index = "shannon")
    shannon_ecosystem_2 = diversity(species_vector_two_ecosystems[2, ], index = "shannon")
    shannon_value = (shannon_ecosystem_1 + shannon_ecosystem_2) / 2
    
    #Alpha diversity: Species richness (mean between the two ecosystems)
    richness_ecosystem_1 = specnumber(species_vector_two_ecosystems[1, ])
    richness_ecosystem_2 = specnumber(species_vector_two_ecosystems[2, ])
    mean_richness_value = (richness_ecosystem_1 + richness_ecosystem_2) / 2
    
    #Beta diversity: Jaccard
    jaccard_index_value = vegdist(species_vector_two_ecosystems,
                                  method = "jaccard") %>%
      as.numeric()
    
    #Beta diversity: Bray Curtis
    bray_curtis_value = vegdist(species_vector_two_ecosystems,
                                method = "bray") %>%
      as.numeric()
    
    #Beta diversity: partitioning of beta diversity from Sorensen index into turnover (Simpson pair-wise dissimilarity) and nestedness (nestedness-fraction of Sorensen)
    betapart_core_object = betapart.core(absence_presence_two_ecosystems)
    beta_spatial_turnover_value = beta.pair(betapart_core_object)$beta.sim %>% as.double()
    beta_nestedness_value = beta.pair(betapart_core_object)$beta.sne %>% as.double()
    beta_total_value = beta.pair(betapart_core_object)$beta.sor %>% as.double()
    
    #Gamma diversity: Meta-ecosystem richness
    metaecosystem_richness_value = colSums(species_vector_two_ecosystems) %>%
      specnumber()
    
    #Put everything together
    ds_metaecosystems[[row_n]] = ds_ecosystems %>%
      filter(culture_ID %in% current_IDs,
             time_point == time_point_input) %>%
      summarise(
        total_metaecosystem_bioarea_mm2 = sum(bioarea_tot_mm2),
        total_metaecosystem_Ble_indiv = sum(Ble_tot_indiv),
        total_metaecosystem_Cep_indiv = sum(Cep_tot_indiv),
        total_metaecosystem_Col_indiv = sum(Col_tot_indiv),
        total_metaecosystem_Eug_indiv = sum(Eug_tot_indiv),
        total_metaecosystem_Eup_indiv = sum(Eup_tot_indiv),
        total_metaecosystem_Lox_indiv = sum(Lox_tot_indiv),
        total_metaecosystem_Pau_indiv = sum(Pau_tot_indiv),
        total_metaecosystem_Pca_indiv = sum(Pca_tot_indiv),
        total_metaecosystem_Spi_indiv = sum(Spi_tot_indiv),
        total_metaecosystem_Spi_te_indiv = sum(Spi_te_tot_indiv),
        total_metaecosystem_Tet_indiv = sum(Tet_tot_indiv)
      ) %>%
      mutate(
        system_nr = current_system_nr,
        ecosystems_combined = current_combination,
        metaecosystem_type = current_metaeco_type,
        disturbance = current_disturbance,
        time_point = time_point_input,
        day = current_day,
        jaccard_index = jaccard_index_value,
        bray_curtis = bray_curtis_value,
        beta_spatial_turnover = beta_spatial_turnover_value,
        beta_nestedness = beta_nestedness_value,
        beta_total = beta_total_value,
        metaecosystem_richness = metaecosystem_richness_value,
        mean_shannon = shannon_value,
        mean_richness = mean_richness_value
      ) %>%
      ungroup()
    
  }
}
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
ds_metaecosystems = ds_metaecosystems %>%
  bind_rows() %>%
  as.data.frame() %>%
  select(
    time_point,
    day,
    system_nr,
    ecosystems_combined,
    disturbance,
    metaecosystem_type,
    mean_shannon,
    mean_richness,
    jaccard_index,
    bray_curtis,
    beta_spatial_turnover,
    beta_nestedness,
    beta_total,
    metaecosystem_richness,
    total_metaecosystem_bioarea_mm2,
    paste0("total_metaecosystem_", protist_species, "_indiv")
  )
expect_equal(nrow(ds_metaecosystems), 
             n_time_points * n_ecosystems_combinations)
#Add column connection

ds_metaecosystems$connection <-
  ifelse(
    ds_metaecosystems$metaecosystem_type %in% c("Medium-Medium unconnected",
                                                "Small-Large unconnected"),
    yes = "unconnected",
    no = "connected"
  )
#Add column ecosystem size symmetry

ds_metaecosystems$ecosystem_size_symmetry <-
  ifelse(
    ds_metaecosystems$metaecosystem_type %in% c("Small-Large unconnected",
                                                "Small-Large meta-ecosystem"),
    yes = "asymmetric",
    no = "symmetric"
  )
#Reorder the meta-ecosystems
ds_metaecosystems = ds_metaecosystems %>%
  mutate(metaecosystem_type = factor(metaecosystem_type,
                                     levels = metaecosystem_types_ordered))
#Join ...
full_join(ds_metaecosystems,
          unconnected_combinations_sets)
## Warning in full_join(ds_metaecosystems, unconnected_combinations_sets): Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 1 of `x` matches multiple rows in `y`.
## ℹ Row 1 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
##   "many-to-many"` to silence this warning.
##      time_point day system_nr ecosystems_combined disturbance
## 1             0   0      1001                1|11         low
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## 1845          4  16      1010                2|15         low
## 1846          4  16      1010                2|15         low
## 1847          4  16      1010                2|15         low
## 1848          4  16      1010                2|15         low
## 1849          5  20      1010                2|15         low
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## 1852          5  20      1010                2|15         low
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## 1871          5  20      1010                2|15         low
## 1872          5  20      1010                2|15         low
## 1873          6  24      1010                2|15         low
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## 1878          6  24      1010                2|15         low
## 1879          6  24      1010                2|15         low
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## 1889          6  24      1010                2|15         low
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## 1893          6  24      1010                2|15         low
## 1894          6  24      1010                2|15         low
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## 1896          6  24      1010                2|15         low
## 1897          7  28      1010                2|15         low
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## 1900          7  28      1010                2|15         low
## 1901          7  28      1010                2|15         low
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## 1909          7  28      1010                2|15         low
## 1910          7  28      1010                2|15         low
## 1911          7  28      1010                2|15         low
## 1912          7  28      1010                2|15         low
## 1913          7  28      1010                2|15         low
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## 1915          7  28      1010                2|15         low
## 1916          7  28      1010                2|15         low
## 1917          7  28      1010                2|15         low
## 1918          7  28      1010                2|15         low
## 1919          7  28      1010                2|15         low
## 1920          7  28      1010                2|15         low
## 1921          0   0      1011                3|11         low
## 1922          0   0      1011                3|11         low
## 1923          0   0      1011                3|11         low
## 1924          0   0      1011                3|11         low
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## 1936          0   0      1011                3|11         low
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## 1939          0   0      1011                3|11         low
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## 1941          0   0      1011                3|11         low
## 1942          0   0      1011                3|11         low
## 1943          0   0      1011                3|11         low
## 1944          0   0      1011                3|11         low
## 1945          1   4      1011                3|11         low
## 1946          1   4      1011                3|11         low
## 1947          1   4      1011                3|11         low
## 1948          1   4      1011                3|11         low
## 1949          1   4      1011                3|11         low
## 1950          1   4      1011                3|11         low
## 1951          1   4      1011                3|11         low
## 1952          1   4      1011                3|11         low
## 1953          1   4      1011                3|11         low
## 1954          1   4      1011                3|11         low
## 1955          1   4      1011                3|11         low
## 1956          1   4      1011                3|11         low
## 1957          1   4      1011                3|11         low
## 1958          1   4      1011                3|11         low
## 1959          1   4      1011                3|11         low
## 1960          1   4      1011                3|11         low
## 1961          1   4      1011                3|11         low
## 1962          1   4      1011                3|11         low
## 1963          1   4      1011                3|11         low
## 1964          1   4      1011                3|11         low
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## 1967          1   4      1011                3|11         low
## 1968          1   4      1011                3|11         low
## 1969          2   8      1011                3|11         low
## 1970          2   8      1011                3|11         low
## 1971          2   8      1011                3|11         low
## 1972          2   8      1011                3|11         low
## 1973          2   8      1011                3|11         low
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## 1975          2   8      1011                3|11         low
## 1976          2   8      1011                3|11         low
## 1977          2   8      1011                3|11         low
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## 1980          2   8      1011                3|11         low
## 1981          2   8      1011                3|11         low
## 1982          2   8      1011                3|11         low
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## 1985          2   8      1011                3|11         low
## 1986          2   8      1011                3|11         low
## 1987          2   8      1011                3|11         low
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## 1989          2   8      1011                3|11         low
## 1990          2   8      1011                3|11         low
## 1991          2   8      1011                3|11         low
## 1992          2   8      1011                3|11         low
## 1993          3  12      1011                3|11         low
## 1994          3  12      1011                3|11         low
## 1995          3  12      1011                3|11         low
## 1996          3  12      1011                3|11         low
## 1997          3  12      1011                3|11         low
## 1998          3  12      1011                3|11         low
## 1999          3  12      1011                3|11         low
## 2000          3  12      1011                3|11         low
## 2001          3  12      1011                3|11         low
## 2002          3  12      1011                3|11         low
## 2003          3  12      1011                3|11         low
## 2004          3  12      1011                3|11         low
## 2005          3  12      1011                3|11         low
## 2006          3  12      1011                3|11         low
## 2007          3  12      1011                3|11         low
## 2008          3  12      1011                3|11         low
## 2009          3  12      1011                3|11         low
## 2010          3  12      1011                3|11         low
## 2011          3  12      1011                3|11         low
## 2012          3  12      1011                3|11         low
## 2013          3  12      1011                3|11         low
## 2014          3  12      1011                3|11         low
## 2015          3  12      1011                3|11         low
## 2016          3  12      1011                3|11         low
## 2017          4  16      1011                3|11         low
## 2018          4  16      1011                3|11         low
## 2019          4  16      1011                3|11         low
## 2020          4  16      1011                3|11         low
## 2021          4  16      1011                3|11         low
## 2022          4  16      1011                3|11         low
## 2023          4  16      1011                3|11         low
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## 2027          4  16      1011                3|11         low
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## 3220          6  24      1017                4|12         low
## 3221          6  24      1017                4|12         low
## 3222          6  24      1017                4|12         low
## 3223          6  24      1017                4|12         low
## 3224          6  24      1017                4|12         low
## 3225          6  24      1017                4|12         low
##           metaecosystem_type mean_shannon mean_richness jaccard_index
## 1    Small-Large unconnected    2.0784670          11.0     0.0000000
## 2    Small-Large unconnected    2.0784670          11.0     0.0000000
## 3    Small-Large unconnected    2.0784670          11.0     0.0000000
## 4    Small-Large unconnected    2.0784670          11.0     0.0000000
## 5    Small-Large unconnected    2.0784670          11.0     0.0000000
## 6    Small-Large unconnected    2.0784670          11.0     0.0000000
## 7    Small-Large unconnected    2.0784670          11.0     0.0000000
## 8    Small-Large unconnected    2.0784670          11.0     0.0000000
## 9    Small-Large unconnected    2.0784670          11.0     0.0000000
## 10   Small-Large unconnected    2.0784670          11.0     0.0000000
## 11   Small-Large unconnected    2.0784670          11.0     0.0000000
## 12   Small-Large unconnected    2.0784670          11.0     0.0000000
## 13   Small-Large unconnected    2.0784670          11.0     0.0000000
## 14   Small-Large unconnected    2.0784670          11.0     0.0000000
## 15   Small-Large unconnected    2.0784670          11.0     0.0000000
## 16   Small-Large unconnected    2.0784670          11.0     0.0000000
## 17   Small-Large unconnected    2.0784670          11.0     0.0000000
## 18   Small-Large unconnected    2.0784670          11.0     0.0000000
## 19   Small-Large unconnected    2.0784670          11.0     0.0000000
## 20   Small-Large unconnected    2.0784670          11.0     0.0000000
## 21   Small-Large unconnected    2.0784670          11.0     0.0000000
## 22   Small-Large unconnected    2.0784670          11.0     0.0000000
## 23   Small-Large unconnected    2.0784670          11.0     0.0000000
## 24   Small-Large unconnected    2.0784670          11.0     0.0000000
## 25   Small-Large unconnected    1.5003642           7.5     0.3797327
## 26   Small-Large unconnected    1.5003642           7.5     0.3797327
## 27   Small-Large unconnected    1.5003642           7.5     0.3797327
## 28   Small-Large unconnected    1.5003642           7.5     0.3797327
## 29   Small-Large unconnected    1.5003642           7.5     0.3797327
## 30   Small-Large unconnected    1.5003642           7.5     0.3797327
## 31   Small-Large unconnected    1.5003642           7.5     0.3797327
## 32   Small-Large unconnected    1.5003642           7.5     0.3797327
## 33   Small-Large unconnected    1.5003642           7.5     0.3797327
## 34   Small-Large unconnected    1.5003642           7.5     0.3797327
## 35   Small-Large unconnected    1.5003642           7.5     0.3797327
## 36   Small-Large unconnected    1.5003642           7.5     0.3797327
## 37   Small-Large unconnected    1.5003642           7.5     0.3797327
## 38   Small-Large unconnected    1.5003642           7.5     0.3797327
## 39   Small-Large unconnected    1.5003642           7.5     0.3797327
## 40   Small-Large unconnected    1.5003642           7.5     0.3797327
## 41   Small-Large unconnected    1.5003642           7.5     0.3797327
## 42   Small-Large unconnected    1.5003642           7.5     0.3797327
## 43   Small-Large unconnected    1.5003642           7.5     0.3797327
## 44   Small-Large unconnected    1.5003642           7.5     0.3797327
## 45   Small-Large unconnected    1.5003642           7.5     0.3797327
## 46   Small-Large unconnected    1.5003642           7.5     0.3797327
## 47   Small-Large unconnected    1.5003642           7.5     0.3797327
## 48   Small-Large unconnected    1.5003642           7.5     0.3797327
## 49   Small-Large unconnected    1.5643953           8.0     0.5027346
## 50   Small-Large unconnected    1.5643953           8.0     0.5027346
## 51   Small-Large unconnected    1.5643953           8.0     0.5027346
## 52   Small-Large unconnected    1.5643953           8.0     0.5027346
## 53   Small-Large unconnected    1.5643953           8.0     0.5027346
## 54   Small-Large unconnected    1.5643953           8.0     0.5027346
## 55   Small-Large unconnected    1.5643953           8.0     0.5027346
## 56   Small-Large unconnected    1.5643953           8.0     0.5027346
## 57   Small-Large unconnected    1.5643953           8.0     0.5027346
## 58   Small-Large unconnected    1.5643953           8.0     0.5027346
## 59   Small-Large unconnected    1.5643953           8.0     0.5027346
## 60   Small-Large unconnected    1.5643953           8.0     0.5027346
## 61   Small-Large unconnected    1.5643953           8.0     0.5027346
## 62   Small-Large unconnected    1.5643953           8.0     0.5027346
## 63   Small-Large unconnected    1.5643953           8.0     0.5027346
## 64   Small-Large unconnected    1.5643953           8.0     0.5027346
## 65   Small-Large unconnected    1.5643953           8.0     0.5027346
## 66   Small-Large unconnected    1.5643953           8.0     0.5027346
## 67   Small-Large unconnected    1.5643953           8.0     0.5027346
## 68   Small-Large unconnected    1.5643953           8.0     0.5027346
## 69   Small-Large unconnected    1.5643953           8.0     0.5027346
## 70   Small-Large unconnected    1.5643953           8.0     0.5027346
## 71   Small-Large unconnected    1.5643953           8.0     0.5027346
## 72   Small-Large unconnected    1.5643953           8.0     0.5027346
## 73   Small-Large unconnected    1.6095690           6.0     0.8561835
## 74   Small-Large unconnected    1.6095690           6.0     0.8561835
## 75   Small-Large unconnected    1.6095690           6.0     0.8561835
## 76   Small-Large unconnected    1.6095690           6.0     0.8561835
## 77   Small-Large unconnected    1.6095690           6.0     0.8561835
## 78   Small-Large unconnected    1.6095690           6.0     0.8561835
## 79   Small-Large unconnected    1.6095690           6.0     0.8561835
## 80   Small-Large unconnected    1.6095690           6.0     0.8561835
## 81   Small-Large unconnected    1.6095690           6.0     0.8561835
## 82   Small-Large unconnected    1.6095690           6.0     0.8561835
## 83   Small-Large unconnected    1.6095690           6.0     0.8561835
## 84   Small-Large unconnected    1.6095690           6.0     0.8561835
## 85   Small-Large unconnected    1.6095690           6.0     0.8561835
## 86   Small-Large unconnected    1.6095690           6.0     0.8561835
## 87   Small-Large unconnected    1.6095690           6.0     0.8561835
## 88   Small-Large unconnected    1.6095690           6.0     0.8561835
## 89   Small-Large unconnected    1.6095690           6.0     0.8561835
## 90   Small-Large unconnected    1.6095690           6.0     0.8561835
## 91   Small-Large unconnected    1.6095690           6.0     0.8561835
## 92   Small-Large unconnected    1.6095690           6.0     0.8561835
## 93   Small-Large unconnected    1.6095690           6.0     0.8561835
## 94   Small-Large unconnected    1.6095690           6.0     0.8561835
## 95   Small-Large unconnected    1.6095690           6.0     0.8561835
## 96   Small-Large unconnected    1.6095690           6.0     0.8561835
## 97   Small-Large unconnected    1.8022460           7.5     0.4038401
## 98   Small-Large unconnected    1.8022460           7.5     0.4038401
## 99   Small-Large unconnected    1.8022460           7.5     0.4038401
## 100  Small-Large unconnected    1.8022460           7.5     0.4038401
## 101  Small-Large unconnected    1.8022460           7.5     0.4038401
## 102  Small-Large unconnected    1.8022460           7.5     0.4038401
## 103  Small-Large unconnected    1.8022460           7.5     0.4038401
## 104  Small-Large unconnected    1.8022460           7.5     0.4038401
## 105  Small-Large unconnected    1.8022460           7.5     0.4038401
## 106  Small-Large unconnected    1.8022460           7.5     0.4038401
## 107  Small-Large unconnected    1.8022460           7.5     0.4038401
## 108  Small-Large unconnected    1.8022460           7.5     0.4038401
## 109  Small-Large unconnected    1.8022460           7.5     0.4038401
## 110  Small-Large unconnected    1.8022460           7.5     0.4038401
## 111  Small-Large unconnected    1.8022460           7.5     0.4038401
## 112  Small-Large unconnected    1.8022460           7.5     0.4038401
## 113  Small-Large unconnected    1.8022460           7.5     0.4038401
## 114  Small-Large unconnected    1.8022460           7.5     0.4038401
## 115  Small-Large unconnected    1.8022460           7.5     0.4038401
## 116  Small-Large unconnected    1.8022460           7.5     0.4038401
## 117  Small-Large unconnected    1.8022460           7.5     0.4038401
## 118  Small-Large unconnected    1.8022460           7.5     0.4038401
## 119  Small-Large unconnected    1.8022460           7.5     0.4038401
## 120  Small-Large unconnected    1.8022460           7.5     0.4038401
## 121  Small-Large unconnected    0.9046531           4.0     0.8022244
## 122  Small-Large unconnected    0.9046531           4.0     0.8022244
## 123  Small-Large unconnected    0.9046531           4.0     0.8022244
## 124  Small-Large unconnected    0.9046531           4.0     0.8022244
## 125  Small-Large unconnected    0.9046531           4.0     0.8022244
## 126  Small-Large unconnected    0.9046531           4.0     0.8022244
## 127  Small-Large unconnected    0.9046531           4.0     0.8022244
## 128  Small-Large unconnected    0.9046531           4.0     0.8022244
## 129  Small-Large unconnected    0.9046531           4.0     0.8022244
## 130  Small-Large unconnected    0.9046531           4.0     0.8022244
## 131  Small-Large unconnected    0.9046531           4.0     0.8022244
## 132  Small-Large unconnected    0.9046531           4.0     0.8022244
## 133  Small-Large unconnected    0.9046531           4.0     0.8022244
## 134  Small-Large unconnected    0.9046531           4.0     0.8022244
## 135  Small-Large unconnected    0.9046531           4.0     0.8022244
## 136  Small-Large unconnected    0.9046531           4.0     0.8022244
## 137  Small-Large unconnected    0.9046531           4.0     0.8022244
## 138  Small-Large unconnected    0.9046531           4.0     0.8022244
## 139  Small-Large unconnected    0.9046531           4.0     0.8022244
## 140  Small-Large unconnected    0.9046531           4.0     0.8022244
## 141  Small-Large unconnected    0.9046531           4.0     0.8022244
## 142  Small-Large unconnected    0.9046531           4.0     0.8022244
## 143  Small-Large unconnected    0.9046531           4.0     0.8022244
## 144  Small-Large unconnected    0.9046531           4.0     0.8022244
## 145  Small-Large unconnected    1.1722772           6.0     0.8009542
## 146  Small-Large unconnected    1.1722772           6.0     0.8009542
## 147  Small-Large unconnected    1.1722772           6.0     0.8009542
## 148  Small-Large unconnected    1.1722772           6.0     0.8009542
## 149  Small-Large unconnected    1.1722772           6.0     0.8009542
## 150  Small-Large unconnected    1.1722772           6.0     0.8009542
## 151  Small-Large unconnected    1.1722772           6.0     0.8009542
## 152  Small-Large unconnected    1.1722772           6.0     0.8009542
## 153  Small-Large unconnected    1.1722772           6.0     0.8009542
## 154  Small-Large unconnected    1.1722772           6.0     0.8009542
## 155  Small-Large unconnected    1.1722772           6.0     0.8009542
## 156  Small-Large unconnected    1.1722772           6.0     0.8009542
## 157  Small-Large unconnected    1.1722772           6.0     0.8009542
## 158  Small-Large unconnected    1.1722772           6.0     0.8009542
## 159  Small-Large unconnected    1.1722772           6.0     0.8009542
## 160  Small-Large unconnected    1.1722772           6.0     0.8009542
## 161  Small-Large unconnected    1.1722772           6.0     0.8009542
## 162  Small-Large unconnected    1.1722772           6.0     0.8009542
## 163  Small-Large unconnected    1.1722772           6.0     0.8009542
## 164  Small-Large unconnected    1.1722772           6.0     0.8009542
## 165  Small-Large unconnected    1.1722772           6.0     0.8009542
## 166  Small-Large unconnected    1.1722772           6.0     0.8009542
## 167  Small-Large unconnected    1.1722772           6.0     0.8009542
## 168  Small-Large unconnected    1.1722772           6.0     0.8009542
## 169  Small-Large unconnected    0.9415572           5.5     0.9159832
## 170  Small-Large unconnected    0.9415572           5.5     0.9159832
## 171  Small-Large unconnected    0.9415572           5.5     0.9159832
## 172  Small-Large unconnected    0.9415572           5.5     0.9159832
## 173  Small-Large unconnected    0.9415572           5.5     0.9159832
## 174  Small-Large unconnected    0.9415572           5.5     0.9159832
## 175  Small-Large unconnected    0.9415572           5.5     0.9159832
## 176  Small-Large unconnected    0.9415572           5.5     0.9159832
## 177  Small-Large unconnected    0.9415572           5.5     0.9159832
## 178  Small-Large unconnected    0.9415572           5.5     0.9159832
## 179  Small-Large unconnected    0.9415572           5.5     0.9159832
## 180  Small-Large unconnected    0.9415572           5.5     0.9159832
## 181  Small-Large unconnected    0.9415572           5.5     0.9159832
## 182  Small-Large unconnected    0.9415572           5.5     0.9159832
## 183  Small-Large unconnected    0.9415572           5.5     0.9159832
## 184  Small-Large unconnected    0.9415572           5.5     0.9159832
## 185  Small-Large unconnected    0.9415572           5.5     0.9159832
## 186  Small-Large unconnected    0.9415572           5.5     0.9159832
## 187  Small-Large unconnected    0.9415572           5.5     0.9159832
## 188  Small-Large unconnected    0.9415572           5.5     0.9159832
## 189  Small-Large unconnected    0.9415572           5.5     0.9159832
## 190  Small-Large unconnected    0.9415572           5.5     0.9159832
## 191  Small-Large unconnected    0.9415572           5.5     0.9159832
## 192  Small-Large unconnected    0.9415572           5.5     0.9159832
## 193  Small-Large unconnected    2.0784670          11.0     0.0000000
## 194  Small-Large unconnected    2.0784670          11.0     0.0000000
## 195  Small-Large unconnected    2.0784670          11.0     0.0000000
## 196  Small-Large unconnected    2.0784670          11.0     0.0000000
## 197  Small-Large unconnected    2.0784670          11.0     0.0000000
## 198  Small-Large unconnected    2.0784670          11.0     0.0000000
## 199  Small-Large unconnected    2.0784670          11.0     0.0000000
## 200  Small-Large unconnected    2.0784670          11.0     0.0000000
## 201  Small-Large unconnected    2.0784670          11.0     0.0000000
## 202  Small-Large unconnected    2.0784670          11.0     0.0000000
## 203  Small-Large unconnected    2.0784670          11.0     0.0000000
## 204  Small-Large unconnected    2.0784670          11.0     0.0000000
## 205  Small-Large unconnected    2.0784670          11.0     0.0000000
## 206  Small-Large unconnected    2.0784670          11.0     0.0000000
## 207  Small-Large unconnected    2.0784670          11.0     0.0000000
## 208  Small-Large unconnected    2.0784670          11.0     0.0000000
## 209  Small-Large unconnected    2.0784670          11.0     0.0000000
## 210  Small-Large unconnected    2.0784670          11.0     0.0000000
## 211  Small-Large unconnected    2.0784670          11.0     0.0000000
## 212  Small-Large unconnected    2.0784670          11.0     0.0000000
## 213  Small-Large unconnected    2.0784670          11.0     0.0000000
## 214  Small-Large unconnected    2.0784670          11.0     0.0000000
## 215  Small-Large unconnected    2.0784670          11.0     0.0000000
## 216  Small-Large unconnected    2.0784670          11.0     0.0000000
## 217  Small-Large unconnected    1.7344675           8.0     0.5863882
## 218  Small-Large unconnected    1.7344675           8.0     0.5863882
## 219  Small-Large unconnected    1.7344675           8.0     0.5863882
## 220  Small-Large unconnected    1.7344675           8.0     0.5863882
## 221  Small-Large unconnected    1.7344675           8.0     0.5863882
## 222  Small-Large unconnected    1.7344675           8.0     0.5863882
## 223  Small-Large unconnected    1.7344675           8.0     0.5863882
## 224  Small-Large unconnected    1.7344675           8.0     0.5863882
## 225  Small-Large unconnected    1.7344675           8.0     0.5863882
## 226  Small-Large unconnected    1.7344675           8.0     0.5863882
## 227  Small-Large unconnected    1.7344675           8.0     0.5863882
## 228  Small-Large unconnected    1.7344675           8.0     0.5863882
## 229  Small-Large unconnected    1.7344675           8.0     0.5863882
## 230  Small-Large unconnected    1.7344675           8.0     0.5863882
## 231  Small-Large unconnected    1.7344675           8.0     0.5863882
## 232  Small-Large unconnected    1.7344675           8.0     0.5863882
## 233  Small-Large unconnected    1.7344675           8.0     0.5863882
## 234  Small-Large unconnected    1.7344675           8.0     0.5863882
## 235  Small-Large unconnected    1.7344675           8.0     0.5863882
## 236  Small-Large unconnected    1.7344675           8.0     0.5863882
## 237  Small-Large unconnected    1.7344675           8.0     0.5863882
## 238  Small-Large unconnected    1.7344675           8.0     0.5863882
## 239  Small-Large unconnected    1.7344675           8.0     0.5863882
## 240  Small-Large unconnected    1.7344675           8.0     0.5863882
## 241  Small-Large unconnected    1.4913521           6.5     0.4020438
## 242  Small-Large unconnected    1.4913521           6.5     0.4020438
## 243  Small-Large unconnected    1.4913521           6.5     0.4020438
## 244  Small-Large unconnected    1.4913521           6.5     0.4020438
## 245  Small-Large unconnected    1.4913521           6.5     0.4020438
## 246  Small-Large unconnected    1.4913521           6.5     0.4020438
## 247  Small-Large unconnected    1.4913521           6.5     0.4020438
## 248  Small-Large unconnected    1.4913521           6.5     0.4020438
## 249  Small-Large unconnected    1.4913521           6.5     0.4020438
## 250  Small-Large unconnected    1.4913521           6.5     0.4020438
## 251  Small-Large unconnected    1.4913521           6.5     0.4020438
## 252  Small-Large unconnected    1.4913521           6.5     0.4020438
## 253  Small-Large unconnected    1.4913521           6.5     0.4020438
## 254  Small-Large unconnected    1.4913521           6.5     0.4020438
## 255  Small-Large unconnected    1.4913521           6.5     0.4020438
## 256  Small-Large unconnected    1.4913521           6.5     0.4020438
## 257  Small-Large unconnected    1.4913521           6.5     0.4020438
## 258  Small-Large unconnected    1.4913521           6.5     0.4020438
## 259  Small-Large unconnected    1.4913521           6.5     0.4020438
## 260  Small-Large unconnected    1.4913521           6.5     0.4020438
## 261  Small-Large unconnected    1.4913521           6.5     0.4020438
## 262  Small-Large unconnected    1.4913521           6.5     0.4020438
## 263  Small-Large unconnected    1.4913521           6.5     0.4020438
## 264  Small-Large unconnected    1.4913521           6.5     0.4020438
## 265  Small-Large unconnected    1.5288340           6.0     0.9015342
## 266  Small-Large unconnected    1.5288340           6.0     0.9015342
## 267  Small-Large unconnected    1.5288340           6.0     0.9015342
## 268  Small-Large unconnected    1.5288340           6.0     0.9015342
## 269  Small-Large unconnected    1.5288340           6.0     0.9015342
## 270  Small-Large unconnected    1.5288340           6.0     0.9015342
## 271  Small-Large unconnected    1.5288340           6.0     0.9015342
## 272  Small-Large unconnected    1.5288340           6.0     0.9015342
## 273  Small-Large unconnected    1.5288340           6.0     0.9015342
## 274  Small-Large unconnected    1.5288340           6.0     0.9015342
## 275  Small-Large unconnected    1.5288340           6.0     0.9015342
## 276  Small-Large unconnected    1.5288340           6.0     0.9015342
## 277  Small-Large unconnected    1.5288340           6.0     0.9015342
## 278  Small-Large unconnected    1.5288340           6.0     0.9015342
## 279  Small-Large unconnected    1.5288340           6.0     0.9015342
## 280  Small-Large unconnected    1.5288340           6.0     0.9015342
## 281  Small-Large unconnected    1.5288340           6.0     0.9015342
## 282  Small-Large unconnected    1.5288340           6.0     0.9015342
## 283  Small-Large unconnected    1.5288340           6.0     0.9015342
## 284  Small-Large unconnected    1.5288340           6.0     0.9015342
## 285  Small-Large unconnected    1.5288340           6.0     0.9015342
## 286  Small-Large unconnected    1.5288340           6.0     0.9015342
## 287  Small-Large unconnected    1.5288340           6.0     0.9015342
## 288  Small-Large unconnected    1.5288340           6.0     0.9015342
## 289  Small-Large unconnected    1.5754616           6.0     0.5594016
## 290  Small-Large unconnected    1.5754616           6.0     0.5594016
## 291  Small-Large unconnected    1.5754616           6.0     0.5594016
## 292  Small-Large unconnected    1.5754616           6.0     0.5594016
## 293  Small-Large unconnected    1.5754616           6.0     0.5594016
## 294  Small-Large unconnected    1.5754616           6.0     0.5594016
## 295  Small-Large unconnected    1.5754616           6.0     0.5594016
## 296  Small-Large unconnected    1.5754616           6.0     0.5594016
## 297  Small-Large unconnected    1.5754616           6.0     0.5594016
## 298  Small-Large unconnected    1.5754616           6.0     0.5594016
## 299  Small-Large unconnected    1.5754616           6.0     0.5594016
## 300  Small-Large unconnected    1.5754616           6.0     0.5594016
## 301  Small-Large unconnected    1.5754616           6.0     0.5594016
## 302  Small-Large unconnected    1.5754616           6.0     0.5594016
## 303  Small-Large unconnected    1.5754616           6.0     0.5594016
## 304  Small-Large unconnected    1.5754616           6.0     0.5594016
## 305  Small-Large unconnected    1.5754616           6.0     0.5594016
## 306  Small-Large unconnected    1.5754616           6.0     0.5594016
## 307  Small-Large unconnected    1.5754616           6.0     0.5594016
## 308  Small-Large unconnected    1.5754616           6.0     0.5594016
## 309  Small-Large unconnected    1.5754616           6.0     0.5594016
## 310  Small-Large unconnected    1.5754616           6.0     0.5594016
## 311  Small-Large unconnected    1.5754616           6.0     0.5594016
## 312  Small-Large unconnected    1.5754616           6.0     0.5594016
## 313  Small-Large unconnected    1.1147692           5.0     0.7862454
## 314  Small-Large unconnected    1.1147692           5.0     0.7862454
## 315  Small-Large unconnected    1.1147692           5.0     0.7862454
## 316  Small-Large unconnected    1.1147692           5.0     0.7862454
## 317  Small-Large unconnected    1.1147692           5.0     0.7862454
## 318  Small-Large unconnected    1.1147692           5.0     0.7862454
## 319  Small-Large unconnected    1.1147692           5.0     0.7862454
## 320  Small-Large unconnected    1.1147692           5.0     0.7862454
## 321  Small-Large unconnected    1.1147692           5.0     0.7862454
## 322  Small-Large unconnected    1.1147692           5.0     0.7862454
## 323  Small-Large unconnected    1.1147692           5.0     0.7862454
## 324  Small-Large unconnected    1.1147692           5.0     0.7862454
## 325  Small-Large unconnected    1.1147692           5.0     0.7862454
## 326  Small-Large unconnected    1.1147692           5.0     0.7862454
## 327  Small-Large unconnected    1.1147692           5.0     0.7862454
## 328  Small-Large unconnected    1.1147692           5.0     0.7862454
## 329  Small-Large unconnected    1.1147692           5.0     0.7862454
## 330  Small-Large unconnected    1.1147692           5.0     0.7862454
## 331  Small-Large unconnected    1.1147692           5.0     0.7862454
## 332  Small-Large unconnected    1.1147692           5.0     0.7862454
## 333  Small-Large unconnected    1.1147692           5.0     0.7862454
## 334  Small-Large unconnected    1.1147692           5.0     0.7862454
## 335  Small-Large unconnected    1.1147692           5.0     0.7862454
## 336  Small-Large unconnected    1.1147692           5.0     0.7862454
## 337  Small-Large unconnected    1.2716771           6.0     0.7890579
## 338  Small-Large unconnected    1.2716771           6.0     0.7890579
## 339  Small-Large unconnected    1.2716771           6.0     0.7890579
## 340  Small-Large unconnected    1.2716771           6.0     0.7890579
## 341  Small-Large unconnected    1.2716771           6.0     0.7890579
## 342  Small-Large unconnected    1.2716771           6.0     0.7890579
## 343  Small-Large unconnected    1.2716771           6.0     0.7890579
## 344  Small-Large unconnected    1.2716771           6.0     0.7890579
## 345  Small-Large unconnected    1.2716771           6.0     0.7890579
## 346  Small-Large unconnected    1.2716771           6.0     0.7890579
## 347  Small-Large unconnected    1.2716771           6.0     0.7890579
## 348  Small-Large unconnected    1.2716771           6.0     0.7890579
## 349  Small-Large unconnected    1.2716771           6.0     0.7890579
## 350  Small-Large unconnected    1.2716771           6.0     0.7890579
## 351  Small-Large unconnected    1.2716771           6.0     0.7890579
## 352  Small-Large unconnected    1.2716771           6.0     0.7890579
## 353  Small-Large unconnected    1.2716771           6.0     0.7890579
## 354  Small-Large unconnected    1.2716771           6.0     0.7890579
## 355  Small-Large unconnected    1.2716771           6.0     0.7890579
## 356  Small-Large unconnected    1.2716771           6.0     0.7890579
## 357  Small-Large unconnected    1.2716771           6.0     0.7890579
## 358  Small-Large unconnected    1.2716771           6.0     0.7890579
## 359  Small-Large unconnected    1.2716771           6.0     0.7890579
## 360  Small-Large unconnected    1.2716771           6.0     0.7890579
## 361  Small-Large unconnected    1.0070034           4.5     0.9160517
## 362  Small-Large unconnected    1.0070034           4.5     0.9160517
## 363  Small-Large unconnected    1.0070034           4.5     0.9160517
## 364  Small-Large unconnected    1.0070034           4.5     0.9160517
## 365  Small-Large unconnected    1.0070034           4.5     0.9160517
## 366  Small-Large unconnected    1.0070034           4.5     0.9160517
## 367  Small-Large unconnected    1.0070034           4.5     0.9160517
## 368  Small-Large unconnected    1.0070034           4.5     0.9160517
## 369  Small-Large unconnected    1.0070034           4.5     0.9160517
## 370  Small-Large unconnected    1.0070034           4.5     0.9160517
## 371  Small-Large unconnected    1.0070034           4.5     0.9160517
## 372  Small-Large unconnected    1.0070034           4.5     0.9160517
## 373  Small-Large unconnected    1.0070034           4.5     0.9160517
## 374  Small-Large unconnected    1.0070034           4.5     0.9160517
## 375  Small-Large unconnected    1.0070034           4.5     0.9160517
## 376  Small-Large unconnected    1.0070034           4.5     0.9160517
## 377  Small-Large unconnected    1.0070034           4.5     0.9160517
## 378  Small-Large unconnected    1.0070034           4.5     0.9160517
## 379  Small-Large unconnected    1.0070034           4.5     0.9160517
## 380  Small-Large unconnected    1.0070034           4.5     0.9160517
## 381  Small-Large unconnected    1.0070034           4.5     0.9160517
## 382  Small-Large unconnected    1.0070034           4.5     0.9160517
## 383  Small-Large unconnected    1.0070034           4.5     0.9160517
## 384  Small-Large unconnected    1.0070034           4.5     0.9160517
## 385  Small-Large unconnected    2.0784670          11.0     0.0000000
## 386  Small-Large unconnected    2.0784670          11.0     0.0000000
## 387  Small-Large unconnected    2.0784670          11.0     0.0000000
## 388  Small-Large unconnected    2.0784670          11.0     0.0000000
## 389  Small-Large unconnected    2.0784670          11.0     0.0000000
## 390  Small-Large unconnected    2.0784670          11.0     0.0000000
## 391  Small-Large unconnected    2.0784670          11.0     0.0000000
## 392  Small-Large unconnected    2.0784670          11.0     0.0000000
## 393  Small-Large unconnected    2.0784670          11.0     0.0000000
## 394  Small-Large unconnected    2.0784670          11.0     0.0000000
## 395  Small-Large unconnected    2.0784670          11.0     0.0000000
## 396  Small-Large unconnected    2.0784670          11.0     0.0000000
## 397  Small-Large unconnected    2.0784670          11.0     0.0000000
## 398  Small-Large unconnected    2.0784670          11.0     0.0000000
## 399  Small-Large unconnected    2.0784670          11.0     0.0000000
## 400  Small-Large unconnected    2.0784670          11.0     0.0000000
## 401  Small-Large unconnected    2.0784670          11.0     0.0000000
## 402  Small-Large unconnected    2.0784670          11.0     0.0000000
## 403  Small-Large unconnected    2.0784670          11.0     0.0000000
## 404  Small-Large unconnected    2.0784670          11.0     0.0000000
## 405  Small-Large unconnected    2.0784670          11.0     0.0000000
## 406  Small-Large unconnected    2.0784670          11.0     0.0000000
## 407  Small-Large unconnected    2.0784670          11.0     0.0000000
## 408  Small-Large unconnected    2.0784670          11.0     0.0000000
## 409  Small-Large unconnected    1.6354094           8.0     0.5434531
## 410  Small-Large unconnected    1.6354094           8.0     0.5434531
## 411  Small-Large unconnected    1.6354094           8.0     0.5434531
## 412  Small-Large unconnected    1.6354094           8.0     0.5434531
## 413  Small-Large unconnected    1.6354094           8.0     0.5434531
## 414  Small-Large unconnected    1.6354094           8.0     0.5434531
## 415  Small-Large unconnected    1.6354094           8.0     0.5434531
## 416  Small-Large unconnected    1.6354094           8.0     0.5434531
## 417  Small-Large unconnected    1.6354094           8.0     0.5434531
## 418  Small-Large unconnected    1.6354094           8.0     0.5434531
## 419  Small-Large unconnected    1.6354094           8.0     0.5434531
## 420  Small-Large unconnected    1.6354094           8.0     0.5434531
## 421  Small-Large unconnected    1.6354094           8.0     0.5434531
## 422  Small-Large unconnected    1.6354094           8.0     0.5434531
## 423  Small-Large unconnected    1.6354094           8.0     0.5434531
## 424  Small-Large unconnected    1.6354094           8.0     0.5434531
## 425  Small-Large unconnected    1.6354094           8.0     0.5434531
## 426  Small-Large unconnected    1.6354094           8.0     0.5434531
## 427  Small-Large unconnected    1.6354094           8.0     0.5434531
## 428  Small-Large unconnected    1.6354094           8.0     0.5434531
## 429  Small-Large unconnected    1.6354094           8.0     0.5434531
## 430  Small-Large unconnected    1.6354094           8.0     0.5434531
## 431  Small-Large unconnected    1.6354094           8.0     0.5434531
## 432  Small-Large unconnected    1.6354094           8.0     0.5434531
## 433  Small-Large unconnected    1.7043816           8.5     0.4219277
## 434  Small-Large unconnected    1.7043816           8.5     0.4219277
## 435  Small-Large unconnected    1.7043816           8.5     0.4219277
## 436  Small-Large unconnected    1.7043816           8.5     0.4219277
## 437  Small-Large unconnected    1.7043816           8.5     0.4219277
## 438  Small-Large unconnected    1.7043816           8.5     0.4219277
## 439  Small-Large unconnected    1.7043816           8.5     0.4219277
## 440  Small-Large unconnected    1.7043816           8.5     0.4219277
## 441  Small-Large unconnected    1.7043816           8.5     0.4219277
## 442  Small-Large unconnected    1.7043816           8.5     0.4219277
## 443  Small-Large unconnected    1.7043816           8.5     0.4219277
## 444  Small-Large unconnected    1.7043816           8.5     0.4219277
## 445  Small-Large unconnected    1.7043816           8.5     0.4219277
## 446  Small-Large unconnected    1.7043816           8.5     0.4219277
## 447  Small-Large unconnected    1.7043816           8.5     0.4219277
## 448  Small-Large unconnected    1.7043816           8.5     0.4219277
## 449  Small-Large unconnected    1.7043816           8.5     0.4219277
## 450  Small-Large unconnected    1.7043816           8.5     0.4219277
## 451  Small-Large unconnected    1.7043816           8.5     0.4219277
## 452  Small-Large unconnected    1.7043816           8.5     0.4219277
## 453  Small-Large unconnected    1.7043816           8.5     0.4219277
## 454  Small-Large unconnected    1.7043816           8.5     0.4219277
## 455  Small-Large unconnected    1.7043816           8.5     0.4219277
## 456  Small-Large unconnected    1.7043816           8.5     0.4219277
## 457  Small-Large unconnected    1.6299430           6.5     0.8561835
## 458  Small-Large unconnected    1.6299430           6.5     0.8561835
## 459  Small-Large unconnected    1.6299430           6.5     0.8561835
## 460  Small-Large unconnected    1.6299430           6.5     0.8561835
## 461  Small-Large unconnected    1.6299430           6.5     0.8561835
## 462  Small-Large unconnected    1.6299430           6.5     0.8561835
## 463  Small-Large unconnected    1.6299430           6.5     0.8561835
## 464  Small-Large unconnected    1.6299430           6.5     0.8561835
## 465  Small-Large unconnected    1.6299430           6.5     0.8561835
## 466  Small-Large unconnected    1.6299430           6.5     0.8561835
## 467  Small-Large unconnected    1.6299430           6.5     0.8561835
## 468  Small-Large unconnected    1.6299430           6.5     0.8561835
## 469  Small-Large unconnected    1.6299430           6.5     0.8561835
## 470  Small-Large unconnected    1.6299430           6.5     0.8561835
## 471  Small-Large unconnected    1.6299430           6.5     0.8561835
## 472  Small-Large unconnected    1.6299430           6.5     0.8561835
## 473  Small-Large unconnected    1.6299430           6.5     0.8561835
## 474  Small-Large unconnected    1.6299430           6.5     0.8561835
## 475  Small-Large unconnected    1.6299430           6.5     0.8561835
## 476  Small-Large unconnected    1.6299430           6.5     0.8561835
## 477  Small-Large unconnected    1.6299430           6.5     0.8561835
## 478  Small-Large unconnected    1.6299430           6.5     0.8561835
## 479  Small-Large unconnected    1.6299430           6.5     0.8561835
## 480  Small-Large unconnected    1.6299430           6.5     0.8561835
## 481  Small-Large unconnected    1.7128054           7.0     0.5498951
## 482  Small-Large unconnected    1.7128054           7.0     0.5498951
## 483  Small-Large unconnected    1.7128054           7.0     0.5498951
## 484  Small-Large unconnected    1.7128054           7.0     0.5498951
## 485  Small-Large unconnected    1.7128054           7.0     0.5498951
## 486  Small-Large unconnected    1.7128054           7.0     0.5498951
## 487  Small-Large unconnected    1.7128054           7.0     0.5498951
## 488  Small-Large unconnected    1.7128054           7.0     0.5498951
## 489  Small-Large unconnected    1.7128054           7.0     0.5498951
## 490  Small-Large unconnected    1.7128054           7.0     0.5498951
## 491  Small-Large unconnected    1.7128054           7.0     0.5498951
## 492  Small-Large unconnected    1.7128054           7.0     0.5498951
## 493  Small-Large unconnected    1.7128054           7.0     0.5498951
## 494  Small-Large unconnected    1.7128054           7.0     0.5498951
## 495  Small-Large unconnected    1.7128054           7.0     0.5498951
## 496  Small-Large unconnected    1.7128054           7.0     0.5498951
## 497  Small-Large unconnected    1.7128054           7.0     0.5498951
## 498  Small-Large unconnected    1.7128054           7.0     0.5498951
## 499  Small-Large unconnected    1.7128054           7.0     0.5498951
## 500  Small-Large unconnected    1.7128054           7.0     0.5498951
## 501  Small-Large unconnected    1.7128054           7.0     0.5498951
## 502  Small-Large unconnected    1.7128054           7.0     0.5498951
## 503  Small-Large unconnected    1.7128054           7.0     0.5498951
## 504  Small-Large unconnected    1.7128054           7.0     0.5498951
## 505  Small-Large unconnected    0.9826256           4.0     0.8091603
## 506  Small-Large unconnected    0.9826256           4.0     0.8091603
## 507  Small-Large unconnected    0.9826256           4.0     0.8091603
## 508  Small-Large unconnected    0.9826256           4.0     0.8091603
## 509  Small-Large unconnected    0.9826256           4.0     0.8091603
## 510  Small-Large unconnected    0.9826256           4.0     0.8091603
## 511  Small-Large unconnected    0.9826256           4.0     0.8091603
## 512  Small-Large unconnected    0.9826256           4.0     0.8091603
## 513  Small-Large unconnected    0.9826256           4.0     0.8091603
## 514  Small-Large unconnected    0.9826256           4.0     0.8091603
## 515  Small-Large unconnected    0.9826256           4.0     0.8091603
## 516  Small-Large unconnected    0.9826256           4.0     0.8091603
## 517  Small-Large unconnected    0.9826256           4.0     0.8091603
## 518  Small-Large unconnected    0.9826256           4.0     0.8091603
## 519  Small-Large unconnected    0.9826256           4.0     0.8091603
## 520  Small-Large unconnected    0.9826256           4.0     0.8091603
## 521  Small-Large unconnected    0.9826256           4.0     0.8091603
## 522  Small-Large unconnected    0.9826256           4.0     0.8091603
## 523  Small-Large unconnected    0.9826256           4.0     0.8091603
## 524  Small-Large unconnected    0.9826256           4.0     0.8091603
## 525  Small-Large unconnected    0.9826256           4.0     0.8091603
## 526  Small-Large unconnected    0.9826256           4.0     0.8091603
## 527  Small-Large unconnected    0.9826256           4.0     0.8091603
## 528  Small-Large unconnected    0.9826256           4.0     0.8091603
## 529  Small-Large unconnected    1.1849855           6.5     0.7669141
## 530  Small-Large unconnected    1.1849855           6.5     0.7669141
## 531  Small-Large unconnected    1.1849855           6.5     0.7669141
## 532  Small-Large unconnected    1.1849855           6.5     0.7669141
## 533  Small-Large unconnected    1.1849855           6.5     0.7669141
## 534  Small-Large unconnected    1.1849855           6.5     0.7669141
## 535  Small-Large unconnected    1.1849855           6.5     0.7669141
## 536  Small-Large unconnected    1.1849855           6.5     0.7669141
## 537  Small-Large unconnected    1.1849855           6.5     0.7669141
## 538  Small-Large unconnected    1.1849855           6.5     0.7669141
## 539  Small-Large unconnected    1.1849855           6.5     0.7669141
## 540  Small-Large unconnected    1.1849855           6.5     0.7669141
## 541  Small-Large unconnected    1.1849855           6.5     0.7669141
## 542  Small-Large unconnected    1.1849855           6.5     0.7669141
## 543  Small-Large unconnected    1.1849855           6.5     0.7669141
## 544  Small-Large unconnected    1.1849855           6.5     0.7669141
## 545  Small-Large unconnected    1.1849855           6.5     0.7669141
## 546  Small-Large unconnected    1.1849855           6.5     0.7669141
## 547  Small-Large unconnected    1.1849855           6.5     0.7669141
## 548  Small-Large unconnected    1.1849855           6.5     0.7669141
## 549  Small-Large unconnected    1.1849855           6.5     0.7669141
## 550  Small-Large unconnected    1.1849855           6.5     0.7669141
## 551  Small-Large unconnected    1.1849855           6.5     0.7669141
## 552  Small-Large unconnected    1.1849855           6.5     0.7669141
## 553  Small-Large unconnected    0.8793394           4.5     0.9340896
## 554  Small-Large unconnected    0.8793394           4.5     0.9340896
## 555  Small-Large unconnected    0.8793394           4.5     0.9340896
## 556  Small-Large unconnected    0.8793394           4.5     0.9340896
## 557  Small-Large unconnected    0.8793394           4.5     0.9340896
## 558  Small-Large unconnected    0.8793394           4.5     0.9340896
## 559  Small-Large unconnected    0.8793394           4.5     0.9340896
## 560  Small-Large unconnected    0.8793394           4.5     0.9340896
## 561  Small-Large unconnected    0.8793394           4.5     0.9340896
## 562  Small-Large unconnected    0.8793394           4.5     0.9340896
## 563  Small-Large unconnected    0.8793394           4.5     0.9340896
## 564  Small-Large unconnected    0.8793394           4.5     0.9340896
## 565  Small-Large unconnected    0.8793394           4.5     0.9340896
## 566  Small-Large unconnected    0.8793394           4.5     0.9340896
## 567  Small-Large unconnected    0.8793394           4.5     0.9340896
## 568  Small-Large unconnected    0.8793394           4.5     0.9340896
## 569  Small-Large unconnected    0.8793394           4.5     0.9340896
## 570  Small-Large unconnected    0.8793394           4.5     0.9340896
## 571  Small-Large unconnected    0.8793394           4.5     0.9340896
## 572  Small-Large unconnected    0.8793394           4.5     0.9340896
## 573  Small-Large unconnected    0.8793394           4.5     0.9340896
## 574  Small-Large unconnected    0.8793394           4.5     0.9340896
## 575  Small-Large unconnected    0.8793394           4.5     0.9340896
## 576  Small-Large unconnected    0.8793394           4.5     0.9340896
## 577  Small-Large unconnected    2.0784670          11.0     0.0000000
## 578  Small-Large unconnected    2.0784670          11.0     0.0000000
## 579  Small-Large unconnected    2.0784670          11.0     0.0000000
## 580  Small-Large unconnected    2.0784670          11.0     0.0000000
## 581  Small-Large unconnected    2.0784670          11.0     0.0000000
## 582  Small-Large unconnected    2.0784670          11.0     0.0000000
## 583  Small-Large unconnected    2.0784670          11.0     0.0000000
## 584  Small-Large unconnected    2.0784670          11.0     0.0000000
## 585  Small-Large unconnected    2.0784670          11.0     0.0000000
## 586  Small-Large unconnected    2.0784670          11.0     0.0000000
## 587  Small-Large unconnected    2.0784670          11.0     0.0000000
## 588  Small-Large unconnected    2.0784670          11.0     0.0000000
## 589  Small-Large unconnected    2.0784670          11.0     0.0000000
## 590  Small-Large unconnected    2.0784670          11.0     0.0000000
## 591  Small-Large unconnected    2.0784670          11.0     0.0000000
## 592  Small-Large unconnected    2.0784670          11.0     0.0000000
## 593  Small-Large unconnected    2.0784670          11.0     0.0000000
## 594  Small-Large unconnected    2.0784670          11.0     0.0000000
## 595  Small-Large unconnected    2.0784670          11.0     0.0000000
## 596  Small-Large unconnected    2.0784670          11.0     0.0000000
## 597  Small-Large unconnected    2.0784670          11.0     0.0000000
## 598  Small-Large unconnected    2.0784670          11.0     0.0000000
## 599  Small-Large unconnected    2.0784670          11.0     0.0000000
## 600  Small-Large unconnected    2.0784670          11.0     0.0000000
## 601  Small-Large unconnected    1.5325570           7.0     0.6161471
## 602  Small-Large unconnected    1.5325570           7.0     0.6161471
## 603  Small-Large unconnected    1.5325570           7.0     0.6161471
## 604  Small-Large unconnected    1.5325570           7.0     0.6161471
## 605  Small-Large unconnected    1.5325570           7.0     0.6161471
## 606  Small-Large unconnected    1.5325570           7.0     0.6161471
## 607  Small-Large unconnected    1.5325570           7.0     0.6161471
## 608  Small-Large unconnected    1.5325570           7.0     0.6161471
## 609  Small-Large unconnected    1.5325570           7.0     0.6161471
## 610  Small-Large unconnected    1.5325570           7.0     0.6161471
## 611  Small-Large unconnected    1.5325570           7.0     0.6161471
## 612  Small-Large unconnected    1.5325570           7.0     0.6161471
## 613  Small-Large unconnected    1.5325570           7.0     0.6161471
## 614  Small-Large unconnected    1.5325570           7.0     0.6161471
## 615  Small-Large unconnected    1.5325570           7.0     0.6161471
## 616  Small-Large unconnected    1.5325570           7.0     0.6161471
## 617  Small-Large unconnected    1.5325570           7.0     0.6161471
## 618  Small-Large unconnected    1.5325570           7.0     0.6161471
## 619  Small-Large unconnected    1.5325570           7.0     0.6161471
## 620  Small-Large unconnected    1.5325570           7.0     0.6161471
## 621  Small-Large unconnected    1.5325570           7.0     0.6161471
## 622  Small-Large unconnected    1.5325570           7.0     0.6161471
## 623  Small-Large unconnected    1.5325570           7.0     0.6161471
## 624  Small-Large unconnected    1.5325570           7.0     0.6161471
## 625  Small-Large unconnected    1.5378489           8.0     0.5443405
## 626  Small-Large unconnected    1.5378489           8.0     0.5443405
## 627  Small-Large unconnected    1.5378489           8.0     0.5443405
## 628  Small-Large unconnected    1.5378489           8.0     0.5443405
## 629  Small-Large unconnected    1.5378489           8.0     0.5443405
## 630  Small-Large unconnected    1.5378489           8.0     0.5443405
## 631  Small-Large unconnected    1.5378489           8.0     0.5443405
## 632  Small-Large unconnected    1.5378489           8.0     0.5443405
## 633  Small-Large unconnected    1.5378489           8.0     0.5443405
## 634  Small-Large unconnected    1.5378489           8.0     0.5443405
## 635  Small-Large unconnected    1.5378489           8.0     0.5443405
## 636  Small-Large unconnected    1.5378489           8.0     0.5443405
## 637  Small-Large unconnected    1.5378489           8.0     0.5443405
## 638  Small-Large unconnected    1.5378489           8.0     0.5443405
## 639  Small-Large unconnected    1.5378489           8.0     0.5443405
## 640  Small-Large unconnected    1.5378489           8.0     0.5443405
## 641  Small-Large unconnected    1.5378489           8.0     0.5443405
## 642  Small-Large unconnected    1.5378489           8.0     0.5443405
## 643  Small-Large unconnected    1.5378489           8.0     0.5443405
## 644  Small-Large unconnected    1.5378489           8.0     0.5443405
## 645  Small-Large unconnected    1.5378489           8.0     0.5443405
## 646  Small-Large unconnected    1.5378489           8.0     0.5443405
## 647  Small-Large unconnected    1.5378489           8.0     0.5443405
## 648  Small-Large unconnected    1.5378489           8.0     0.5443405
## 649  Small-Large unconnected    1.2717353           5.0     0.8062622
## 650  Small-Large unconnected    1.2717353           5.0     0.8062622
## 651  Small-Large unconnected    1.2717353           5.0     0.8062622
## 652  Small-Large unconnected    1.2717353           5.0     0.8062622
## 653  Small-Large unconnected    1.2717353           5.0     0.8062622
## 654  Small-Large unconnected    1.2717353           5.0     0.8062622
## 655  Small-Large unconnected    1.2717353           5.0     0.8062622
## 656  Small-Large unconnected    1.2717353           5.0     0.8062622
## 657  Small-Large unconnected    1.2717353           5.0     0.8062622
## 658  Small-Large unconnected    1.2717353           5.0     0.8062622
## 659  Small-Large unconnected    1.2717353           5.0     0.8062622
## 660  Small-Large unconnected    1.2717353           5.0     0.8062622
## 661  Small-Large unconnected    1.2717353           5.0     0.8062622
## 662  Small-Large unconnected    1.2717353           5.0     0.8062622
## 663  Small-Large unconnected    1.2717353           5.0     0.8062622
## 664  Small-Large unconnected    1.2717353           5.0     0.8062622
## 665  Small-Large unconnected    1.2717353           5.0     0.8062622
## 666  Small-Large unconnected    1.2717353           5.0     0.8062622
## 667  Small-Large unconnected    1.2717353           5.0     0.8062622
## 668  Small-Large unconnected    1.2717353           5.0     0.8062622
## 669  Small-Large unconnected    1.2717353           5.0     0.8062622
## 670  Small-Large unconnected    1.2717353           5.0     0.8062622
## 671  Small-Large unconnected    1.2717353           5.0     0.8062622
## 672  Small-Large unconnected    1.2717353           5.0     0.8062622
## 673  Small-Large unconnected    1.5711195           6.5     0.5964585
## 674  Small-Large unconnected    1.5711195           6.5     0.5964585
## 675  Small-Large unconnected    1.5711195           6.5     0.5964585
## 676  Small-Large unconnected    1.5711195           6.5     0.5964585
## 677  Small-Large unconnected    1.5711195           6.5     0.5964585
## 678  Small-Large unconnected    1.5711195           6.5     0.5964585
## 679  Small-Large unconnected    1.5711195           6.5     0.5964585
## 680  Small-Large unconnected    1.5711195           6.5     0.5964585
## 681  Small-Large unconnected    1.5711195           6.5     0.5964585
## 682  Small-Large unconnected    1.5711195           6.5     0.5964585
## 683  Small-Large unconnected    1.5711195           6.5     0.5964585
## 684  Small-Large unconnected    1.5711195           6.5     0.5964585
## 685  Small-Large unconnected    1.5711195           6.5     0.5964585
## 686  Small-Large unconnected    1.5711195           6.5     0.5964585
## 687  Small-Large unconnected    1.5711195           6.5     0.5964585
## 688  Small-Large unconnected    1.5711195           6.5     0.5964585
## 689  Small-Large unconnected    1.5711195           6.5     0.5964585
## 690  Small-Large unconnected    1.5711195           6.5     0.5964585
## 691  Small-Large unconnected    1.5711195           6.5     0.5964585
## 692  Small-Large unconnected    1.5711195           6.5     0.5964585
## 693  Small-Large unconnected    1.5711195           6.5     0.5964585
## 694  Small-Large unconnected    1.5711195           6.5     0.5964585
## 695  Small-Large unconnected    1.5711195           6.5     0.5964585
## 696  Small-Large unconnected    1.5711195           6.5     0.5964585
## 697  Small-Large unconnected    0.9613777           3.5     0.7674121
## 698  Small-Large unconnected    0.9613777           3.5     0.7674121
## 699  Small-Large unconnected    0.9613777           3.5     0.7674121
## 700  Small-Large unconnected    0.9613777           3.5     0.7674121
## 701  Small-Large unconnected    0.9613777           3.5     0.7674121
## 702  Small-Large unconnected    0.9613777           3.5     0.7674121
## 703  Small-Large unconnected    0.9613777           3.5     0.7674121
## 704  Small-Large unconnected    0.9613777           3.5     0.7674121
## 705  Small-Large unconnected    0.9613777           3.5     0.7674121
## 706  Small-Large unconnected    0.9613777           3.5     0.7674121
## 707  Small-Large unconnected    0.9613777           3.5     0.7674121
## 708  Small-Large unconnected    0.9613777           3.5     0.7674121
## 709  Small-Large unconnected    0.9613777           3.5     0.7674121
## 710  Small-Large unconnected    0.9613777           3.5     0.7674121
## 711  Small-Large unconnected    0.9613777           3.5     0.7674121
## 712  Small-Large unconnected    0.9613777           3.5     0.7674121
## 713  Small-Large unconnected    0.9613777           3.5     0.7674121
## 714  Small-Large unconnected    0.9613777           3.5     0.7674121
## 715  Small-Large unconnected    0.9613777           3.5     0.7674121
## 716  Small-Large unconnected    0.9613777           3.5     0.7674121
## 717  Small-Large unconnected    0.9613777           3.5     0.7674121
## 718  Small-Large unconnected    0.9613777           3.5     0.7674121
## 719  Small-Large unconnected    0.9613777           3.5     0.7674121
## 720  Small-Large unconnected    0.9613777           3.5     0.7674121
## 721  Small-Large unconnected    1.3870793           5.5     0.6086957
## 722  Small-Large unconnected    1.3870793           5.5     0.6086957
## 723  Small-Large unconnected    1.3870793           5.5     0.6086957
## 724  Small-Large unconnected    1.3870793           5.5     0.6086957
## 725  Small-Large unconnected    1.3870793           5.5     0.6086957
## 726  Small-Large unconnected    1.3870793           5.5     0.6086957
## 727  Small-Large unconnected    1.3870793           5.5     0.6086957
## 728  Small-Large unconnected    1.3870793           5.5     0.6086957
## 729  Small-Large unconnected    1.3870793           5.5     0.6086957
## 730  Small-Large unconnected    1.3870793           5.5     0.6086957
## 731  Small-Large unconnected    1.3870793           5.5     0.6086957
## 732  Small-Large unconnected    1.3870793           5.5     0.6086957
## 733  Small-Large unconnected    1.3870793           5.5     0.6086957
## 734  Small-Large unconnected    1.3870793           5.5     0.6086957
## 735  Small-Large unconnected    1.3870793           5.5     0.6086957
## 736  Small-Large unconnected    1.3870793           5.5     0.6086957
## 737  Small-Large unconnected    1.3870793           5.5     0.6086957
## 738  Small-Large unconnected    1.3870793           5.5     0.6086957
## 739  Small-Large unconnected    1.3870793           5.5     0.6086957
## 740  Small-Large unconnected    1.3870793           5.5     0.6086957
## 741  Small-Large unconnected    1.3870793           5.5     0.6086957
## 742  Small-Large unconnected    1.3870793           5.5     0.6086957
## 743  Small-Large unconnected    1.3870793           5.5     0.6086957
## 744  Small-Large unconnected    1.3870793           5.5     0.6086957
## 745  Small-Large unconnected    0.9302665           3.5     0.6133333
## 746  Small-Large unconnected    0.9302665           3.5     0.6133333
## 747  Small-Large unconnected    0.9302665           3.5     0.6133333
## 748  Small-Large unconnected    0.9302665           3.5     0.6133333
## 749  Small-Large unconnected    0.9302665           3.5     0.6133333
## 750  Small-Large unconnected    0.9302665           3.5     0.6133333
## 751  Small-Large unconnected    0.9302665           3.5     0.6133333
## 752  Small-Large unconnected    0.9302665           3.5     0.6133333
## 753  Small-Large unconnected    0.9302665           3.5     0.6133333
## 754  Small-Large unconnected    0.9302665           3.5     0.6133333
## 755  Small-Large unconnected    0.9302665           3.5     0.6133333
## 756  Small-Large unconnected    0.9302665           3.5     0.6133333
## 757  Small-Large unconnected    0.9302665           3.5     0.6133333
## 758  Small-Large unconnected    0.9302665           3.5     0.6133333
## 759  Small-Large unconnected    0.9302665           3.5     0.6133333
## 760  Small-Large unconnected    0.9302665           3.5     0.6133333
## 761  Small-Large unconnected    0.9302665           3.5     0.6133333
## 762  Small-Large unconnected    0.9302665           3.5     0.6133333
## 763  Small-Large unconnected    0.9302665           3.5     0.6133333
## 764  Small-Large unconnected    0.9302665           3.5     0.6133333
## 765  Small-Large unconnected    0.9302665           3.5     0.6133333
## 766  Small-Large unconnected    0.9302665           3.5     0.6133333
## 767  Small-Large unconnected    0.9302665           3.5     0.6133333
## 768  Small-Large unconnected    0.9302665           3.5     0.6133333
## 769  Small-Large unconnected    2.0784670          11.0     0.0000000
## 770  Small-Large unconnected    2.0784670          11.0     0.0000000
## 771  Small-Large unconnected    2.0784670          11.0     0.0000000
## 772  Small-Large unconnected    2.0784670          11.0     0.0000000
## 773  Small-Large unconnected    2.0784670          11.0     0.0000000
## 774  Small-Large unconnected    2.0784670          11.0     0.0000000
## 775  Small-Large unconnected    2.0784670          11.0     0.0000000
## 776  Small-Large unconnected    2.0784670          11.0     0.0000000
## 777  Small-Large unconnected    2.0784670          11.0     0.0000000
## 778  Small-Large unconnected    2.0784670          11.0     0.0000000
## 779  Small-Large unconnected    2.0784670          11.0     0.0000000
## 780  Small-Large unconnected    2.0784670          11.0     0.0000000
## 781  Small-Large unconnected    2.0784670          11.0     0.0000000
## 782  Small-Large unconnected    2.0784670          11.0     0.0000000
## 783  Small-Large unconnected    2.0784670          11.0     0.0000000
## 784  Small-Large unconnected    2.0784670          11.0     0.0000000
## 785  Small-Large unconnected    2.0784670          11.0     0.0000000
## 786  Small-Large unconnected    2.0784670          11.0     0.0000000
## 787  Small-Large unconnected    2.0784670          11.0     0.0000000
## 788  Small-Large unconnected    2.0784670          11.0     0.0000000
## 789  Small-Large unconnected    2.0784670          11.0     0.0000000
## 790  Small-Large unconnected    2.0784670          11.0     0.0000000
## 791  Small-Large unconnected    2.0784670          11.0     0.0000000
## 792  Small-Large unconnected    2.0784670          11.0     0.0000000
## 793  Small-Large unconnected    1.7576182           8.0     0.6485050
## 794  Small-Large unconnected    1.7576182           8.0     0.6485050
## 795  Small-Large unconnected    1.7576182           8.0     0.6485050
## 796  Small-Large unconnected    1.7576182           8.0     0.6485050
## 797  Small-Large unconnected    1.7576182           8.0     0.6485050
## 798  Small-Large unconnected    1.7576182           8.0     0.6485050
## 799  Small-Large unconnected    1.7576182           8.0     0.6485050
## 800  Small-Large unconnected    1.7576182           8.0     0.6485050
## 801  Small-Large unconnected    1.7576182           8.0     0.6485050
## 802  Small-Large unconnected    1.7576182           8.0     0.6485050
## 803  Small-Large unconnected    1.7576182           8.0     0.6485050
## 804  Small-Large unconnected    1.7576182           8.0     0.6485050
## 805  Small-Large unconnected    1.7576182           8.0     0.6485050
## 806  Small-Large unconnected    1.7576182           8.0     0.6485050
## 807  Small-Large unconnected    1.7576182           8.0     0.6485050
## 808  Small-Large unconnected    1.7576182           8.0     0.6485050
## 809  Small-Large unconnected    1.7576182           8.0     0.6485050
## 810  Small-Large unconnected    1.7576182           8.0     0.6485050
## 811  Small-Large unconnected    1.7576182           8.0     0.6485050
## 812  Small-Large unconnected    1.7576182           8.0     0.6485050
## 813  Small-Large unconnected    1.7576182           8.0     0.6485050
## 814  Small-Large unconnected    1.7576182           8.0     0.6485050
## 815  Small-Large unconnected    1.7576182           8.0     0.6485050
## 816  Small-Large unconnected    1.7576182           8.0     0.6485050
## 817  Small-Large unconnected    1.6208829           7.5     0.5405548
## 818  Small-Large unconnected    1.6208829           7.5     0.5405548
## 819  Small-Large unconnected    1.6208829           7.5     0.5405548
## 820  Small-Large unconnected    1.6208829           7.5     0.5405548
## 821  Small-Large unconnected    1.6208829           7.5     0.5405548
## 822  Small-Large unconnected    1.6208829           7.5     0.5405548
## 823  Small-Large unconnected    1.6208829           7.5     0.5405548
## 824  Small-Large unconnected    1.6208829           7.5     0.5405548
## 825  Small-Large unconnected    1.6208829           7.5     0.5405548
## 826  Small-Large unconnected    1.6208829           7.5     0.5405548
## 827  Small-Large unconnected    1.6208829           7.5     0.5405548
## 828  Small-Large unconnected    1.6208829           7.5     0.5405548
## 829  Small-Large unconnected    1.6208829           7.5     0.5405548
## 830  Small-Large unconnected    1.6208829           7.5     0.5405548
## 831  Small-Large unconnected    1.6208829           7.5     0.5405548
## 832  Small-Large unconnected    1.6208829           7.5     0.5405548
## 833  Small-Large unconnected    1.6208829           7.5     0.5405548
## 834  Small-Large unconnected    1.6208829           7.5     0.5405548
## 835  Small-Large unconnected    1.6208829           7.5     0.5405548
## 836  Small-Large unconnected    1.6208829           7.5     0.5405548
## 837  Small-Large unconnected    1.6208829           7.5     0.5405548
## 838  Small-Large unconnected    1.6208829           7.5     0.5405548
## 839  Small-Large unconnected    1.6208829           7.5     0.5405548
## 840  Small-Large unconnected    1.6208829           7.5     0.5405548
## 841  Small-Large unconnected    1.5861251           6.0     0.8562784
## 842  Small-Large unconnected    1.5861251           6.0     0.8562784
## 843  Small-Large unconnected    1.5861251           6.0     0.8562784
## 844  Small-Large unconnected    1.5861251           6.0     0.8562784
## 845  Small-Large unconnected    1.5861251           6.0     0.8562784
## 846  Small-Large unconnected    1.5861251           6.0     0.8562784
## 847  Small-Large unconnected    1.5861251           6.0     0.8562784
## 848  Small-Large unconnected    1.5861251           6.0     0.8562784
## 849  Small-Large unconnected    1.5861251           6.0     0.8562784
## 850  Small-Large unconnected    1.5861251           6.0     0.8562784
## 851  Small-Large unconnected    1.5861251           6.0     0.8562784
## 852  Small-Large unconnected    1.5861251           6.0     0.8562784
## 853  Small-Large unconnected    1.5861251           6.0     0.8562784
## 854  Small-Large unconnected    1.5861251           6.0     0.8562784
## 855  Small-Large unconnected    1.5861251           6.0     0.8562784
## 856  Small-Large unconnected    1.5861251           6.0     0.8562784
## 857  Small-Large unconnected    1.5861251           6.0     0.8562784
## 858  Small-Large unconnected    1.5861251           6.0     0.8562784
## 859  Small-Large unconnected    1.5861251           6.0     0.8562784
## 860  Small-Large unconnected    1.5861251           6.0     0.8562784
## 861  Small-Large unconnected    1.5861251           6.0     0.8562784
## 862  Small-Large unconnected    1.5861251           6.0     0.8562784
## 863  Small-Large unconnected    1.5861251           6.0     0.8562784
## 864  Small-Large unconnected    1.5861251           6.0     0.8562784
## 865  Small-Large unconnected    1.6705149           7.5     0.5076640
## 866  Small-Large unconnected    1.6705149           7.5     0.5076640
## 867  Small-Large unconnected    1.6705149           7.5     0.5076640
## 868  Small-Large unconnected    1.6705149           7.5     0.5076640
## 869  Small-Large unconnected    1.6705149           7.5     0.5076640
## 870  Small-Large unconnected    1.6705149           7.5     0.5076640
## 871  Small-Large unconnected    1.6705149           7.5     0.5076640
## 872  Small-Large unconnected    1.6705149           7.5     0.5076640
## 873  Small-Large unconnected    1.6705149           7.5     0.5076640
## 874  Small-Large unconnected    1.6705149           7.5     0.5076640
## 875  Small-Large unconnected    1.6705149           7.5     0.5076640
## 876  Small-Large unconnected    1.6705149           7.5     0.5076640
## 877  Small-Large unconnected    1.6705149           7.5     0.5076640
## 878  Small-Large unconnected    1.6705149           7.5     0.5076640
## 879  Small-Large unconnected    1.6705149           7.5     0.5076640
## 880  Small-Large unconnected    1.6705149           7.5     0.5076640
## 881  Small-Large unconnected    1.6705149           7.5     0.5076640
## 882  Small-Large unconnected    1.6705149           7.5     0.5076640
## 883  Small-Large unconnected    1.6705149           7.5     0.5076640
## 884  Small-Large unconnected    1.6705149           7.5     0.5076640
## 885  Small-Large unconnected    1.6705149           7.5     0.5076640
## 886  Small-Large unconnected    1.6705149           7.5     0.5076640
## 887  Small-Large unconnected    1.6705149           7.5     0.5076640
## 888  Small-Large unconnected    1.6705149           7.5     0.5076640
## 889  Small-Large unconnected    1.1807457           5.0     0.8075314
## 890  Small-Large unconnected    1.1807457           5.0     0.8075314
## 891  Small-Large unconnected    1.1807457           5.0     0.8075314
## 892  Small-Large unconnected    1.1807457           5.0     0.8075314
## 893  Small-Large unconnected    1.1807457           5.0     0.8075314
## 894  Small-Large unconnected    1.1807457           5.0     0.8075314
## 895  Small-Large unconnected    1.1807457           5.0     0.8075314
## 896  Small-Large unconnected    1.1807457           5.0     0.8075314
## 897  Small-Large unconnected    1.1807457           5.0     0.8075314
## 898  Small-Large unconnected    1.1807457           5.0     0.8075314
## 899  Small-Large unconnected    1.1807457           5.0     0.8075314
## 900  Small-Large unconnected    1.1807457           5.0     0.8075314
## 901  Small-Large unconnected    1.1807457           5.0     0.8075314
## 902  Small-Large unconnected    1.1807457           5.0     0.8075314
## 903  Small-Large unconnected    1.1807457           5.0     0.8075314
## 904  Small-Large unconnected    1.1807457           5.0     0.8075314
## 905  Small-Large unconnected    1.1807457           5.0     0.8075314
## 906  Small-Large unconnected    1.1807457           5.0     0.8075314
## 907  Small-Large unconnected    1.1807457           5.0     0.8075314
## 908  Small-Large unconnected    1.1807457           5.0     0.8075314
## 909  Small-Large unconnected    1.1807457           5.0     0.8075314
## 910  Small-Large unconnected    1.1807457           5.0     0.8075314
## 911  Small-Large unconnected    1.1807457           5.0     0.8075314
## 912  Small-Large unconnected    1.1807457           5.0     0.8075314
## 913  Small-Large unconnected    1.5071598           6.5     0.8093303
## 914  Small-Large unconnected    1.5071598           6.5     0.8093303
## 915  Small-Large unconnected    1.5071598           6.5     0.8093303
## 916  Small-Large unconnected    1.5071598           6.5     0.8093303
## 917  Small-Large unconnected    1.5071598           6.5     0.8093303
## 918  Small-Large unconnected    1.5071598           6.5     0.8093303
## 919  Small-Large unconnected    1.5071598           6.5     0.8093303
## 920  Small-Large unconnected    1.5071598           6.5     0.8093303
## 921  Small-Large unconnected    1.5071598           6.5     0.8093303
## 922  Small-Large unconnected    1.5071598           6.5     0.8093303
## 923  Small-Large unconnected    1.5071598           6.5     0.8093303
## 924  Small-Large unconnected    1.5071598           6.5     0.8093303
## 925  Small-Large unconnected    1.5071598           6.5     0.8093303
## 926  Small-Large unconnected    1.5071598           6.5     0.8093303
## 927  Small-Large unconnected    1.5071598           6.5     0.8093303
## 928  Small-Large unconnected    1.5071598           6.5     0.8093303
## 929  Small-Large unconnected    1.5071598           6.5     0.8093303
## 930  Small-Large unconnected    1.5071598           6.5     0.8093303
## 931  Small-Large unconnected    1.5071598           6.5     0.8093303
## 932  Small-Large unconnected    1.5071598           6.5     0.8093303
## 933  Small-Large unconnected    1.5071598           6.5     0.8093303
## 934  Small-Large unconnected    1.5071598           6.5     0.8093303
## 935  Small-Large unconnected    1.5071598           6.5     0.8093303
## 936  Small-Large unconnected    1.5071598           6.5     0.8093303
## 937  Small-Large unconnected    0.9391687           5.0     0.9203269
## 938  Small-Large unconnected    0.9391687           5.0     0.9203269
## 939  Small-Large unconnected    0.9391687           5.0     0.9203269
## 940  Small-Large unconnected    0.9391687           5.0     0.9203269
## 941  Small-Large unconnected    0.9391687           5.0     0.9203269
## 942  Small-Large unconnected    0.9391687           5.0     0.9203269
## 943  Small-Large unconnected    0.9391687           5.0     0.9203269
## 944  Small-Large unconnected    0.9391687           5.0     0.9203269
## 945  Small-Large unconnected    0.9391687           5.0     0.9203269
## 946  Small-Large unconnected    0.9391687           5.0     0.9203269
## 947  Small-Large unconnected    0.9391687           5.0     0.9203269
## 948  Small-Large unconnected    0.9391687           5.0     0.9203269
## 949  Small-Large unconnected    0.9391687           5.0     0.9203269
## 950  Small-Large unconnected    0.9391687           5.0     0.9203269
## 951  Small-Large unconnected    0.9391687           5.0     0.9203269
## 952  Small-Large unconnected    0.9391687           5.0     0.9203269
## 953  Small-Large unconnected    0.9391687           5.0     0.9203269
## 954  Small-Large unconnected    0.9391687           5.0     0.9203269
## 955  Small-Large unconnected    0.9391687           5.0     0.9203269
## 956  Small-Large unconnected    0.9391687           5.0     0.9203269
## 957  Small-Large unconnected    0.9391687           5.0     0.9203269
## 958  Small-Large unconnected    0.9391687           5.0     0.9203269
## 959  Small-Large unconnected    0.9391687           5.0     0.9203269
## 960  Small-Large unconnected    0.9391687           5.0     0.9203269
## 961  Small-Large unconnected    2.0784670          11.0     0.0000000
## 962  Small-Large unconnected    2.0784670          11.0     0.0000000
## 963  Small-Large unconnected    2.0784670          11.0     0.0000000
## 964  Small-Large unconnected    2.0784670          11.0     0.0000000
## 965  Small-Large unconnected    2.0784670          11.0     0.0000000
## 966  Small-Large unconnected    2.0784670          11.0     0.0000000
## 967  Small-Large unconnected    2.0784670          11.0     0.0000000
## 968  Small-Large unconnected    2.0784670          11.0     0.0000000
## 969  Small-Large unconnected    2.0784670          11.0     0.0000000
## 970  Small-Large unconnected    2.0784670          11.0     0.0000000
## 971  Small-Large unconnected    2.0784670          11.0     0.0000000
## 972  Small-Large unconnected    2.0784670          11.0     0.0000000
## 973  Small-Large unconnected    2.0784670          11.0     0.0000000
## 974  Small-Large unconnected    2.0784670          11.0     0.0000000
## 975  Small-Large unconnected    2.0784670          11.0     0.0000000
## 976  Small-Large unconnected    2.0784670          11.0     0.0000000
## 977  Small-Large unconnected    2.0784670          11.0     0.0000000
## 978  Small-Large unconnected    2.0784670          11.0     0.0000000
## 979  Small-Large unconnected    2.0784670          11.0     0.0000000
## 980  Small-Large unconnected    2.0784670          11.0     0.0000000
## 981  Small-Large unconnected    2.0784670          11.0     0.0000000
## 982  Small-Large unconnected    2.0784670          11.0     0.0000000
## 983  Small-Large unconnected    2.0784670          11.0     0.0000000
## 984  Small-Large unconnected    2.0784670          11.0     0.0000000
## 985  Small-Large unconnected    1.5540186           8.0     0.4775502
## 986  Small-Large unconnected    1.5540186           8.0     0.4775502
## 987  Small-Large unconnected    1.5540186           8.0     0.4775502
## 988  Small-Large unconnected    1.5540186           8.0     0.4775502
## 989  Small-Large unconnected    1.5540186           8.0     0.4775502
## 990  Small-Large unconnected    1.5540186           8.0     0.4775502
## 991  Small-Large unconnected    1.5540186           8.0     0.4775502
## 992  Small-Large unconnected    1.5540186           8.0     0.4775502
## 993  Small-Large unconnected    1.5540186           8.0     0.4775502
## 994  Small-Large unconnected    1.5540186           8.0     0.4775502
## 995  Small-Large unconnected    1.5540186           8.0     0.4775502
## 996  Small-Large unconnected    1.5540186           8.0     0.4775502
## 997  Small-Large unconnected    1.5540186           8.0     0.4775502
## 998  Small-Large unconnected    1.5540186           8.0     0.4775502
## 999  Small-Large unconnected    1.5540186           8.0     0.4775502
## 1000 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1001 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1002 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1003 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1004 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1005 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1006 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1007 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1008 Small-Large unconnected    1.5540186           8.0     0.4775502
## 1009 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1010 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1011 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1012 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1013 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1014 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1015 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1016 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1017 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1018 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1019 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1020 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1021 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1022 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1023 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1024 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1025 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1026 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1027 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1028 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1029 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1030 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1031 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1032 Small-Large unconnected    1.5213817           8.5     0.6802785
## 1033 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1034 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1035 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1036 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1037 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1038 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1039 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1040 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1041 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1042 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1043 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1044 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1045 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1046 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1047 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1048 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1049 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1050 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1051 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1052 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1053 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1054 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1055 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1056 Small-Large unconnected    1.7632593           7.0     0.4519279
## 1057 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1058 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1059 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1060 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1061 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1062 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1063 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1064 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1065 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1066 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1067 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1068 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1069 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1070 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1071 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1072 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1073 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1074 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1075 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1076 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1077 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1078 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1079 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1080 Small-Large unconnected    1.3837136           5.5     0.6129142
## 1081 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1082 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1083 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1084 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1085 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1086 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1087 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1088 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1089 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1090 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1091 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1092 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1093 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1094 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1095 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1096 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1097 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1098 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1099 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1100 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1101 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1102 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1103 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1104 Small-Large unconnected    1.1906786           4.5     0.9314463
## 1105 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1106 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1107 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1108 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1109 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1110 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1111 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1112 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1113 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1114 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1115 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1116 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1117 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1118 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1119 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1120 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1121 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1122 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1123 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1124 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1125 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1126 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1127 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1128 Small-Large unconnected    0.5580146           4.0     0.8940736
## 1129 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1130 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1131 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1132 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1133 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1134 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1135 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1136 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1137 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1138 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1139 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1140 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1141 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1142 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1143 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1144 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1145 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1146 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1147 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1148 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1149 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1150 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1151 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1152 Small-Large unconnected    0.6573424           5.0     0.9461440
## 1153 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1154 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1155 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1156 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1157 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1158 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1159 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1160 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1161 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1162 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1163 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1164 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1165 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1166 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1167 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1168 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1169 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1170 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1171 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1172 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1173 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1174 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1175 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1176 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1177 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1178 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1179 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1180 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1181 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1182 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1183 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1184 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1185 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1186 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1187 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1188 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1189 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1190 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1191 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1192 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1193 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1194 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1195 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1196 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1197 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1198 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1199 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1200 Small-Large unconnected    1.7881218           8.5     0.4851643
## 1201 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1202 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1203 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1204 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1205 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1206 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1207 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1208 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1209 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1210 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1211 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1212 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1213 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1214 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1215 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1216 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1217 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1218 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1219 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1220 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1221 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1222 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1223 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1224 Small-Large unconnected    1.4483385           7.0     0.6127187
## 1225 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1226 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1227 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1228 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1229 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1230 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1231 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1232 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1233 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1234 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1235 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1236 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1237 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1238 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1239 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1240 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1241 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1242 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1243 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1244 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1245 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1246 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1247 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1248 Small-Large unconnected    1.6825243           7.0     0.5191233
## 1249 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1250 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1251 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1252 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1253 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1254 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1255 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1256 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1257 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1258 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1259 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1260 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1261 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1262 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1263 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1264 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1265 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1266 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1267 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1268 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1269 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1270 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1271 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1272 Small-Large unconnected    1.1569293           4.0     0.7495992
## 1273 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1274 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1275 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1276 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1277 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1278 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1279 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1280 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1281 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1282 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1283 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1284 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1285 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1286 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1287 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1288 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1289 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1290 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1291 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1292 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1293 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1294 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1295 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1296 Small-Large unconnected    1.4007946           5.5     0.8509009
## 1297 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1298 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1299 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1300 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1301 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1302 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1303 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1304 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1305 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1306 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1307 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1308 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1309 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1310 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1311 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1312 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1313 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1314 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1315 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1316 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1317 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1318 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1319 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1320 Small-Large unconnected    0.6574145           4.0     0.8908058
## 1321 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1322 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1323 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1324 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1325 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1326 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1327 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1328 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1329 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1330 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1331 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1332 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1333 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1334 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1335 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1336 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1337 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1338 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1339 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1340 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1341 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1342 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1343 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1344 Small-Large unconnected    0.7227886           4.0     0.9301829
## 1345 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1346 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1347 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1348 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1349 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1350 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1351 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1352 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1353 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1354 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1355 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1356 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1357 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1358 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1359 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1360 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1361 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1362 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1363 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1364 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1365 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1366 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1367 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1368 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1369 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1370 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1371 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1372 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1373 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1374 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1375 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1376 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1377 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1378 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1379 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1380 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1381 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1382 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1383 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1384 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1385 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1386 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1387 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1388 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1389 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1390 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1391 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1392 Small-Large unconnected    1.6890637           8.5     0.5151939
## 1393 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1394 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1395 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1396 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1397 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1398 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1399 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1400 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1401 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1402 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1403 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1404 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1405 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1406 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1407 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1408 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1409 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1410 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1411 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1412 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1413 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1414 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1415 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1416 Small-Large unconnected    1.6613680           9.0     0.6067317
## 1417 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1418 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1419 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1420 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1421 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1422 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1423 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1424 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1425 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1426 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1427 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1428 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1429 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1430 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1431 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1432 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1433 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1434 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1435 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1436 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1437 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1438 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1439 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1440 Small-Large unconnected    1.7836333           7.5     0.5057999
## 1441 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1442 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1443 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1444 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1445 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1446 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1447 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1448 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1449 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1450 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1451 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1452 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1453 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1454 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1455 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1456 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1457 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1458 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1459 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1460 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1461 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1462 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1463 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1464 Small-Large unconnected    1.2942730           5.0     0.7453294
## 1465 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1466 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1467 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1468 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1469 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1470 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1471 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1472 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1473 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1474 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1475 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1476 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1477 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1478 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1479 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1480 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1481 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1482 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1483 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1484 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1485 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1486 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1487 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1488 Small-Large unconnected    1.2686511           4.5     0.9064490
## 1489 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1490 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1491 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1492 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1493 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1494 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1495 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1496 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1497 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1498 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1499 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1500 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1501 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1502 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1503 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1504 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1505 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1506 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1507 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1508 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1509 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1510 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1511 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1512 Small-Large unconnected    0.5707230           4.5     0.8832972
## 1513 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1514 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1515 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1516 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1517 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1518 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1519 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1520 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1521 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1522 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1523 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1524 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1525 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1526 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1527 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1528 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1529 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1530 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1531 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1532 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1533 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1534 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1535 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1536 Small-Large unconnected    0.5951247           4.0     0.9576002
## 1537 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1538 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1539 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1540 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1541 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1542 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1543 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1544 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1545 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1546 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1547 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1548 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1549 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1550 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1551 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1552 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1553 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1554 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1555 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1556 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1557 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1558 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1559 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1560 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1561 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1562 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1563 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1564 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1565 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1566 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1567 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1568 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1569 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1570 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1571 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1572 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1573 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1574 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1575 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1576 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1577 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1578 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1579 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1580 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1581 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1582 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1583 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1584 Small-Large unconnected    1.5862113           7.5     0.3935303
## 1585 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1586 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1587 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1588 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1589 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1590 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1591 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1592 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1593 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1594 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1595 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1596 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1597 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1598 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1599 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1600 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1601 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1602 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1603 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1604 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1605 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1606 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1607 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1608 Small-Large unconnected    1.4948352           8.5     0.6102781
## 1609 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1610 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1611 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1612 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1613 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1614 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1615 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1616 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1617 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1618 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1619 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1620 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1621 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1622 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1623 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1624 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1625 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1626 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1627 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1628 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1629 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1630 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1631 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1632 Small-Large unconnected    1.4254256           6.0     0.5077328
## 1633 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1634 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1635 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1636 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1637 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1638 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1639 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1640 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1641 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1642 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1643 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1644 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1645 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1646 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1647 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1648 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1649 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1650 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1651 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1652 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1653 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1654 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1655 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1656 Small-Large unconnected    1.1525871           4.5     0.7699053
## 1657 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1658 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1659 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1660 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1661 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1662 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1663 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1664 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1665 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1666 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1667 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1668 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1669 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1670 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1671 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1672 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1673 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1674 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1675 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1676 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1677 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1678 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1679 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1680 Small-Large unconnected    1.2474031           4.0     0.9374289
## 1681 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1682 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1683 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1684 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1685 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1686 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1687 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1688 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1689 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1690 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1691 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1692 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1693 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1694 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1695 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1696 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1697 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1698 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1699 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1700 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1701 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1702 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1703 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1704 Small-Large unconnected    0.7728167           3.5     0.7388350
## 1705 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1706 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1707 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1708 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1709 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1710 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1711 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1712 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1713 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1714 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1715 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1716 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1717 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1718 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1719 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1720 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1721 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1722 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1723 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1724 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1725 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1726 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1727 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1728 Small-Large unconnected    0.6460517           3.0     0.7497872
## 1729 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1730 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1731 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1732 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1733 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1734 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1735 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1736 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1737 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1738 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1739 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1740 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1741 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1742 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1743 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1744 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1745 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1746 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1747 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1748 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1749 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1750 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1751 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1752 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1753 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1754 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1755 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1756 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1757 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1758 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1759 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1760 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1761 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1762 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1763 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1764 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1765 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1766 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1767 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1768 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1769 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1770 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1771 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1772 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1773 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1774 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1775 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1776 Small-Large unconnected    1.8112725           8.5     0.5241108
## 1777 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1778 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1779 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1780 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1781 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1782 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1783 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1784 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1785 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1786 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1787 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1788 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1789 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1790 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1791 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1792 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1793 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1794 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1795 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1796 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1797 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1798 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1799 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1800 Small-Large unconnected    1.5778693           8.0     0.7006088
## 1801 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1802 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1803 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1804 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1805 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1806 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1807 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1808 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1809 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1810 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1811 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1812 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1813 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1814 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1815 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1816 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1817 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1818 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1819 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1820 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1821 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1822 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1823 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1824 Small-Large unconnected    1.7398154           7.0     0.4756098
## 1825 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1826 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1827 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1828 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1829 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1830 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1831 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1832 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1833 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1834 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1835 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1836 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1837 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1838 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1839 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1840 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1841 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1842 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1843 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1844 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1845 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1846 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1847 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1848 Small-Large unconnected    1.2519825           5.5     0.7460988
## 1849 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1850 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1851 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1852 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1853 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1854 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1855 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1856 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1857 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1858 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1859 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1860 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1861 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1862 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1863 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1864 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1865 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1866 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1867 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1868 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1869 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1870 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1871 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1872 Small-Large unconnected    1.4667712           5.5     0.9079875
## 1873 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1874 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1875 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1876 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1877 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1878 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1879 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1880 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1881 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1882 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1883 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1884 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1885 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1886 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1887 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1888 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1889 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1890 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1891 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1892 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1893 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1894 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1895 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1896 Small-Large unconnected    0.8928972           4.5     0.9027828
## 1897 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1898 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1899 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1900 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1901 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1902 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1903 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1904 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1905 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1906 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1907 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1908 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1909 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1910 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1911 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1912 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1913 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1914 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1915 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1916 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1917 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1918 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1919 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1920 Small-Large unconnected    0.6549539           4.5     0.9497693
## 1921 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1922 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1923 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1924 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1925 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1926 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1927 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1928 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1929 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1930 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1931 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1932 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1933 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1934 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1935 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1936 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1937 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1938 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1939 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1940 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1941 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1942 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1943 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1944 Small-Large unconnected    2.0784670          11.0     0.0000000
## 1945 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1946 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1947 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1948 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1949 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1950 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1951 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1952 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1953 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1954 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1955 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1956 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1957 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1958 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1959 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1960 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1961 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1962 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1963 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1964 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1965 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1966 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1967 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1968 Small-Large unconnected    1.4587022           7.0     0.4647482
## 1969 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1970 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1971 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1972 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1973 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1974 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1975 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1976 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1977 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1978 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1979 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1980 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1981 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1982 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1983 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1984 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1985 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1986 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1987 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1988 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1989 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1990 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1991 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1992 Small-Large unconnected    1.4635307           7.0     0.5222681
## 1993 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1994 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1995 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1996 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1997 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1998 Small-Large unconnected    1.4969088           6.0     0.6928848
## 1999 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2000 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2001 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2002 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2003 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2004 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2005 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2006 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2007 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2008 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2009 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2010 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2011 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2012 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2013 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2014 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2015 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2016 Small-Large unconnected    1.4969088           6.0     0.6928848
## 2017 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2018 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2019 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2020 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2021 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2022 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2023 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2024 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2025 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2026 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2027 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2028 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2029 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2030 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2031 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2032 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2033 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2034 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2035 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2036 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2037 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2038 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2039 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2040 Small-Large unconnected    1.4098276           6.0     0.6760997
## 2041 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2042 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2043 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2044 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2045 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2046 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2047 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2048 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2049 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2050 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2051 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2052 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2053 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2054 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2055 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2056 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2057 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2058 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2059 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2060 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2061 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2062 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2063 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2064 Small-Large unconnected    0.8677885           4.0     0.8623853
## 2065 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2066 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2067 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2068 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2069 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2070 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2071 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2072 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2073 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2074 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2075 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2076 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2077 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2078 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2079 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2080 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2081 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2082 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2083 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2084 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2085 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2086 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2087 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2088 Small-Large unconnected    1.0349319           5.0     0.8940736
## 2089 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2090 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2091 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2092 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2093 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2094 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2095 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2096 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2097 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2098 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2099 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2100 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2101 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2102 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2103 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2104 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2105 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2106 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2107 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2108 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2109 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2110 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2111 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2112 Small-Large unconnected    0.8886913           5.5     0.8939828
## 2113 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2114 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2115 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2116 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2117 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2118 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2119 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2120 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2121 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2122 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2123 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2124 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2125 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2126 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2127 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2128 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2129 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2130 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2131 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2132 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2133 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2134 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2135 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2136 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2137 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2138 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2139 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2140 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2141 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2142 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2143 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2144 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2145 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2146 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2147 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2148 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2149 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2150 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2151 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2152 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2153 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2154 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2155 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2156 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2157 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2158 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2159 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2160 Small-Large unconnected    1.6928054           7.5     0.5989357
## 2161 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2162 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2163 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2164 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2165 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2166 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2167 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2168 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2169 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2170 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2171 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2172 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2173 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2174 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2175 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2176 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2177 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2178 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2179 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2180 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2181 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2182 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2183 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2184 Small-Large unconnected    1.3904874           5.5     0.2931267
## 2185 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2186 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2187 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2188 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2189 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2190 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2191 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2192 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2193 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2194 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2195 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2196 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2197 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2198 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2199 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2200 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2201 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2202 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2203 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2204 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2205 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2206 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2207 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2208 Small-Large unconnected    1.4161738           6.0     0.5734298
## 2209 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2210 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2211 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2212 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2213 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2214 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2215 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2216 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2217 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2218 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2219 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2220 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2221 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2222 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2223 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2224 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2225 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2226 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2227 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2228 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2229 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2230 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2231 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2232 Small-Large unconnected    1.1830432           4.5     0.5461783
## 2233 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2234 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2235 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2236 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2237 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2238 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2239 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2240 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2241 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2242 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2243 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2244 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2245 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2246 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2247 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2248 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2249 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2250 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2251 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2252 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2253 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2254 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2255 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2256 Small-Large unconnected    1.0779045           5.0     0.8424721
## 2257 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2258 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2259 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2260 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2261 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2262 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2263 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2264 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2265 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2266 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2267 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2268 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2269 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2270 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2271 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2272 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2273 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2274 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2275 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2276 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2277 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2278 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2279 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2280 Small-Large unconnected    1.1343318           5.0     0.9128705
## 2281 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2282 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2283 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2284 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2285 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2286 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2287 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2288 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2289 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2290 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2291 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2292 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2293 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2294 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2295 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2296 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2297 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2298 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2299 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2300 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2301 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2302 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2303 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2304 Small-Large unconnected    0.9541375           4.5     0.8634686
## 2305 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2306 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2307 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2308 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2309 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2310 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2311 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2312 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2313 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2314 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2315 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2316 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2317 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2318 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2319 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2320 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2321 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2322 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2323 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2324 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2325 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2326 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2327 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2328 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2329 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2330 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2331 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2332 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2333 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2334 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2335 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2336 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2337 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2338 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2339 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2340 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2341 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2342 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2343 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2344 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2345 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2346 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2347 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2348 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2349 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2350 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2351 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2352 Small-Large unconnected    1.5937474           7.5     0.3858672
## 2353 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2354 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2355 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2356 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2357 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2358 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2359 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2360 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2361 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2362 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2363 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2364 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2365 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2366 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2367 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2368 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2369 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2370 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2371 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2372 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2373 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2374 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2375 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2376 Small-Large unconnected    1.6035169           7.5     0.3980177
## 2377 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2378 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2379 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2380 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2381 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2382 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2383 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2384 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2385 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2386 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2387 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2388 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2389 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2390 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2391 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2392 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2393 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2394 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2395 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2396 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2397 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2398 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2399 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2400 Small-Large unconnected    1.5172828           6.5     0.6578032
## 2401 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2402 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2403 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2404 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2405 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2406 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2407 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2408 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2409 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2410 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2411 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2412 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2413 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2414 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2415 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2416 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2417 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2418 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2419 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2420 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2421 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2422 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2423 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2424 Small-Large unconnected    1.3203870           5.5     0.5871069
## 2425 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2426 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2427 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2428 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2429 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2430 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2431 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2432 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2433 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2434 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2435 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2436 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2437 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2438 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2439 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2440 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2441 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2442 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2443 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2444 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2445 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2446 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2447 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2448 Small-Large unconnected    0.9457610           4.0     0.8813489
## 2449 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2450 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2451 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2452 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2453 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2454 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2455 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2456 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2457 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2458 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2459 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2460 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2461 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2462 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2463 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2464 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2465 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2466 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2467 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2468 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2469 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2470 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2471 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2472 Small-Large unconnected    1.0476403           5.5     0.8832972
## 2473 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2474 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2475 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2476 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2477 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2478 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2479 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2480 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2481 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2482 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2483 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2484 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2485 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2486 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2487 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2488 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2489 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2490 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2491 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2492 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2493 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2494 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2495 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2496 Small-Large unconnected    0.8264735           4.5     0.9161354
## 2497 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2498 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2499 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2500 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2501 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2502 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2503 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2504 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2505 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2506 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2507 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2508 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2509 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2510 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2511 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2512 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2513 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2514 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2515 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2516 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2517 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2518 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2519 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2520 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2521 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2522 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2523 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2524 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2525 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2526 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2527 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2528 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2529 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2530 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2531 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2532 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2533 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2534 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2535 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2536 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2537 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2538 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2539 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2540 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2541 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2542 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2543 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2544 Small-Large unconnected    1.4908950           6.5     0.4258033
## 2545 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2546 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2547 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2548 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2549 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2550 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2551 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2552 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2553 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2554 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2555 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2556 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2557 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2558 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2559 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2560 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2561 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2562 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2563 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2564 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2565 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2566 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2567 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2568 Small-Large unconnected    1.4369842           7.0     0.5152690
## 2569 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2570 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2571 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2572 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2573 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2574 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2575 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2576 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2577 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2578 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2579 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2580 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2581 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2582 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2583 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2584 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2585 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2586 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2587 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2588 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2589 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2590 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2591 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2592 Small-Large unconnected    1.1590750           5.0     0.3094595
## 2593 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2594 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2595 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2596 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2597 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2598 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2599 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2600 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2601 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2602 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2603 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2604 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2605 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2606 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2607 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2608 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2609 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2610 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2611 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2612 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2613 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2614 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2615 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2616 Small-Large unconnected    1.1787010           5.0     0.5881557
## 2617 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2618 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2619 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2620 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2621 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2622 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2623 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2624 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2625 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2626 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2627 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2628 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2629 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2630 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2631 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2632 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2633 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2634 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2635 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2636 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2637 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2638 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2639 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2640 Small-Large unconnected    0.9245130           3.5     0.8128693
## 2641 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2642 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2643 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2644 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2645 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2646 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2647 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2648 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2649 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2650 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2651 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2652 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2653 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2654 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2655 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2656 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2657 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2658 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2659 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2660 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2661 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2662 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2663 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2664 Small-Large unconnected    1.2497340           4.5     0.8109840
## 2665 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2666 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2667 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2668 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2669 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2670 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2671 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2672 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2673 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2674 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2675 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2676 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2677 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2678 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2679 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2680 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2681 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2682 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2683 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2684 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2685 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2686 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2687 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2688 Small-Large unconnected    0.8774006           3.5     0.7224848
## 2689 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2690 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2691 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2692 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2693 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2694 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2695 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2696 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2697 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2698 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2699 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2700 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2701 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2702 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2703 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2704 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2705 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2706 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2707 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2708 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2709 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2710 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2711 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2712 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2713 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2714 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2715 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2716 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2717 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2718 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2719 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2720 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2721 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2722 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2723 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2724 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2725 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2726 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2727 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2728 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2729 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2730 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2731 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2732 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2733 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2734 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2735 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2736 Small-Large unconnected    1.7159561           7.5     0.6949506
## 2737 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2738 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2739 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2740 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2741 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2742 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2743 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2744 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2745 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2746 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2747 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2748 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2749 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2750 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2751 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2752 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2753 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2754 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2755 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2756 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2757 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2758 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2759 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2760 Small-Large unconnected    1.5200182           6.5     0.4408897
## 2761 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2762 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2763 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2764 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2765 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2766 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2767 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2768 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2769 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2770 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2771 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2772 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2773 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2774 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2775 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2776 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2777 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2778 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2779 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2780 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2781 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2782 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2783 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2784 Small-Large unconnected    1.4734648           6.0     0.5394322
## 2785 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2786 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2787 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2788 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2789 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2790 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2791 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2792 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2793 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2794 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2795 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2796 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2797 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2798 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2799 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2800 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2801 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2802 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2803 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2804 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2805 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2806 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2807 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2808 Small-Large unconnected    1.2780964           6.0     0.5398773
## 2809 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2810 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2811 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2812 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2813 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2814 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2815 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2816 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2817 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2818 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2819 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2820 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2821 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2822 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2823 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2824 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2825 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2826 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2827 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2828 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2829 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2830 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2831 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2832 Small-Large unconnected    1.1438811           5.0     0.8833879
## 2833 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2834 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2835 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2836 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2837 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2838 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2839 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2840 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2841 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2842 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2843 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2844 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2845 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2846 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2847 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2848 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2849 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2850 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2851 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2852 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2853 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2854 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2855 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2856 Small-Large unconnected    1.3698145           5.5     0.9027828
## 2857 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2858 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2859 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2860 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2861 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2862 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2863 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2864 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2865 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2866 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2867 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2868 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2869 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2870 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2871 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2872 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2873 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2874 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2875 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2876 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2877 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2878 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2879 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2880 Small-Large unconnected    0.8863028           5.0     0.9009702
## 2881 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2882 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2883 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2884 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2885 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2886 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2887 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2888 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2889 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2890 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2891 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2892 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2893 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2894 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2895 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2896 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2897 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2898 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2899 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2900 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2901 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2902 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2903 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2904 Small-Large unconnected    2.0784670          11.0     0.0000000
## 2905 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2906 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2907 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2908 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2909 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2910 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2911 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2912 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2913 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2914 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2915 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2916 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2917 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2918 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2919 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2920 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2921 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2922 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2923 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2924 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2925 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2926 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2927 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2928 Small-Large unconnected    1.4093629           7.5     0.3571855
## 2929 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2930 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2931 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2932 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2933 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2934 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2935 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2936 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2937 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2938 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2939 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2940 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2941 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2942 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2943 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2944 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2945 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2946 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2947 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2948 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2949 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2950 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2951 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2952 Small-Large unconnected    1.5566020           8.0     0.4330945
## 2953 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2954 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2955 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2956 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2957 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2958 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2959 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2960 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2961 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2962 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2963 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2964 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2965 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2966 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2967 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2968 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2969 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2970 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2971 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2972 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2973 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2974 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2975 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2976 Small-Large unconnected    1.3271205           5.0     0.7095691
## 2977 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2978 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2979 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2980 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2981 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2982 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2983 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2984 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2985 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2986 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2987 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2988 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2989 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2990 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2991 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2992 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2993 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2994 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2995 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2996 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2997 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2998 Small-Large unconnected    1.4700682           6.0     0.5603006
## 2999 Small-Large unconnected    1.4700682           6.0     0.5603006
## 3000 Small-Large unconnected    1.4700682           6.0     0.5603006
## 3001 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3002 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3003 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3004 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3005 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3006 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3007 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3008 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3009 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3010 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3011 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3012 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3013 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3014 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3015 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3016 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3017 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3018 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3019 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3020 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3021 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3022 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3023 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3024 Small-Large unconnected    1.0940609           4.5     0.8165592
## 3025 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3026 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3027 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3028 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3029 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3030 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3031 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3032 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3033 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3034 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3035 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3036 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3037 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3038 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3039 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3040 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3041 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3042 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3043 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3044 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3045 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3046 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3047 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3048 Small-Large unconnected    0.8851120           4.5     0.9186702
## 3049 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3050 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3051 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3052 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3053 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3054 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3055 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3056 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3057 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3058 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3059 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3060 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3061 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3062 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3063 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3064 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3065 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3066 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3067 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3068 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3069 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3070 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3071 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3072 Small-Large unconnected    1.3912750           7.0     0.8836783
## 3073 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3074 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3075 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3076 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3077 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3078 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3079 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3080 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3081 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3082 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3083 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3084 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3085 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3086 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3087 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3088 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3089 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3090 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3091 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3092 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3093 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3094 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3095 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3096 Small-Large unconnected    2.0784670          11.0     0.0000000
## 3097 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3098 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3099 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3100 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3101 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3102 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3103 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3104 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3105 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3106 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3107 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3108 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3109 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3110 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3111 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3112 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3113 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3114 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3115 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3116 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3117 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3118 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3119 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3120 Small-Large unconnected    1.6434662           8.0     0.6412607
## 3121 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3122 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3123 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3124 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3125 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3126 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3127 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3128 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3129 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3130 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3131 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3132 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3133 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3134 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3135 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3136 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3137 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3138 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3139 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3140 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3141 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3142 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3143 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3144 Small-Large unconnected    1.4835587           6.5     0.3623978
## 3145 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3146 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3147 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3148 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3149 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3150 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3151 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3152 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3153 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3154 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3155 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3156 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3157 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3158 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3159 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3160 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3161 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3162 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3163 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3164 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3165 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3166 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3167 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3168 Small-Large unconnected    1.2463855           5.0     0.7793072
## 3169 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3170 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3171 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3172 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3173 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3174 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3175 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3176 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3177 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3178 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3179 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3180 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3181 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3182 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3183 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3184 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3185 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3186 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3187 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3188 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3189 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3190 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3191 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3192 Small-Large unconnected    1.2432838           4.5     0.6892984
## 3193 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3194 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3195 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3196 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3197 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3198 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3199 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3200 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3201 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3202 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3203 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3204 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3205 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3206 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3207 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3208 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3209 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3210 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3211 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3212 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3213 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3214 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3215 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3216 Small-Large unconnected    1.3041770           5.5     0.8280669
## 3217 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3218 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3219 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3220 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3221 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3222 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3223 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3224 Small-Large unconnected    0.9845120           4.5     0.8706428
## 3225 Small-Large unconnected    0.9845120           4.5     0.8706428
##      bray_curtis beta_spatial_turnover beta_nestedness beta_total
## 1      0.0000000             0.0000000      0.00000000 0.00000000
## 2      0.0000000             0.0000000      0.00000000 0.00000000
## 3      0.0000000             0.0000000      0.00000000 0.00000000
## 4      0.0000000             0.0000000      0.00000000 0.00000000
## 5      0.0000000             0.0000000      0.00000000 0.00000000
## 6      0.0000000             0.0000000      0.00000000 0.00000000
## 7      0.0000000             0.0000000      0.00000000 0.00000000
## 8      0.0000000             0.0000000      0.00000000 0.00000000
## 9      0.0000000             0.0000000      0.00000000 0.00000000
## 10     0.0000000             0.0000000      0.00000000 0.00000000
## 11     0.0000000             0.0000000      0.00000000 0.00000000
## 12     0.0000000             0.0000000      0.00000000 0.00000000
## 13     0.0000000             0.0000000      0.00000000 0.00000000
## 14     0.0000000             0.0000000      0.00000000 0.00000000
## 15     0.0000000             0.0000000      0.00000000 0.00000000
## 16     0.0000000             0.0000000      0.00000000 0.00000000
## 17     0.0000000             0.0000000      0.00000000 0.00000000
## 18     0.0000000             0.0000000      0.00000000 0.00000000
## 19     0.0000000             0.0000000      0.00000000 0.00000000
## 20     0.0000000             0.0000000      0.00000000 0.00000000
## 21     0.0000000             0.0000000      0.00000000 0.00000000
## 22     0.0000000             0.0000000      0.00000000 0.00000000
## 23     0.0000000             0.0000000      0.00000000 0.00000000
## 24     0.0000000             0.0000000      0.00000000 0.00000000
## 25     0.2343643             0.1428571      0.05714286 0.20000000
## 26     0.2343643             0.1428571      0.05714286 0.20000000
## 27     0.2343643             0.1428571      0.05714286 0.20000000
## 28     0.2343643             0.1428571      0.05714286 0.20000000
## 29     0.2343643             0.1428571      0.05714286 0.20000000
## 30     0.2343643             0.1428571      0.05714286 0.20000000
## 31     0.2343643             0.1428571      0.05714286 0.20000000
## 32     0.2343643             0.1428571      0.05714286 0.20000000
## 33     0.2343643             0.1428571      0.05714286 0.20000000
## 34     0.2343643             0.1428571      0.05714286 0.20000000
## 35     0.2343643             0.1428571      0.05714286 0.20000000
## 36     0.2343643             0.1428571      0.05714286 0.20000000
## 37     0.2343643             0.1428571      0.05714286 0.20000000
## 38     0.2343643             0.1428571      0.05714286 0.20000000
## 39     0.2343643             0.1428571      0.05714286 0.20000000
## 40     0.2343643             0.1428571      0.05714286 0.20000000
## 41     0.2343643             0.1428571      0.05714286 0.20000000
## 42     0.2343643             0.1428571      0.05714286 0.20000000
## 43     0.2343643             0.1428571      0.05714286 0.20000000
## 44     0.2343643             0.1428571      0.05714286 0.20000000
## 45     0.2343643             0.1428571      0.05714286 0.20000000
## 46     0.2343643             0.1428571      0.05714286 0.20000000
## 47     0.2343643             0.1428571      0.05714286 0.20000000
## 48     0.2343643             0.1428571      0.05714286 0.20000000
## 49     0.3357686             0.1250000      0.00000000 0.12500000
## 50     0.3357686             0.1250000      0.00000000 0.12500000
## 51     0.3357686             0.1250000      0.00000000 0.12500000
## 52     0.3357686             0.1250000      0.00000000 0.12500000
## 53     0.3357686             0.1250000      0.00000000 0.12500000
## 54     0.3357686             0.1250000      0.00000000 0.12500000
## 55     0.3357686             0.1250000      0.00000000 0.12500000
## 56     0.3357686             0.1250000      0.00000000 0.12500000
## 57     0.3357686             0.1250000      0.00000000 0.12500000
## 58     0.3357686             0.1250000      0.00000000 0.12500000
## 59     0.3357686             0.1250000      0.00000000 0.12500000
## 60     0.3357686             0.1250000      0.00000000 0.12500000
## 61     0.3357686             0.1250000      0.00000000 0.12500000
## 62     0.3357686             0.1250000      0.00000000 0.12500000
## 63     0.3357686             0.1250000      0.00000000 0.12500000
## 64     0.3357686             0.1250000      0.00000000 0.12500000
## 65     0.3357686             0.1250000      0.00000000 0.12500000
## 66     0.3357686             0.1250000      0.00000000 0.12500000
## 67     0.3357686             0.1250000      0.00000000 0.12500000
## 68     0.3357686             0.1250000      0.00000000 0.12500000
## 69     0.3357686             0.1250000      0.00000000 0.12500000
## 70     0.3357686             0.1250000      0.00000000 0.12500000
## 71     0.3357686             0.1250000      0.00000000 0.12500000
## 72     0.3357686             0.1250000      0.00000000 0.12500000
## 73     0.7485323             0.0000000      0.33333333 0.33333333
## 74     0.7485323             0.0000000      0.33333333 0.33333333
## 75     0.7485323             0.0000000      0.33333333 0.33333333
## 76     0.7485323             0.0000000      0.33333333 0.33333333
## 77     0.7485323             0.0000000      0.33333333 0.33333333
## 78     0.7485323             0.0000000      0.33333333 0.33333333
## 79     0.7485323             0.0000000      0.33333333 0.33333333
## 80     0.7485323             0.0000000      0.33333333 0.33333333
## 81     0.7485323             0.0000000      0.33333333 0.33333333
## 82     0.7485323             0.0000000      0.33333333 0.33333333
## 83     0.7485323             0.0000000      0.33333333 0.33333333
## 84     0.7485323             0.0000000      0.33333333 0.33333333
## 85     0.7485323             0.0000000      0.33333333 0.33333333
## 86     0.7485323             0.0000000      0.33333333 0.33333333
## 87     0.7485323             0.0000000      0.33333333 0.33333333
## 88     0.7485323             0.0000000      0.33333333 0.33333333
## 89     0.7485323             0.0000000      0.33333333 0.33333333
## 90     0.7485323             0.0000000      0.33333333 0.33333333
## 91     0.7485323             0.0000000      0.33333333 0.33333333
## 92     0.7485323             0.0000000      0.33333333 0.33333333
## 93     0.7485323             0.0000000      0.33333333 0.33333333
## 94     0.7485323             0.0000000      0.33333333 0.33333333
## 95     0.7485323             0.0000000      0.33333333 0.33333333
## 96     0.7485323             0.0000000      0.33333333 0.33333333
## 97     0.2530073             0.1428571      0.05714286 0.20000000
## 98     0.2530073             0.1428571      0.05714286 0.20000000
## 99     0.2530073             0.1428571      0.05714286 0.20000000
## 100    0.2530073             0.1428571      0.05714286 0.20000000
## 101    0.2530073             0.1428571      0.05714286 0.20000000
## 102    0.2530073             0.1428571      0.05714286 0.20000000
## 103    0.2530073             0.1428571      0.05714286 0.20000000
## 104    0.2530073             0.1428571      0.05714286 0.20000000
## 105    0.2530073             0.1428571      0.05714286 0.20000000
## 106    0.2530073             0.1428571      0.05714286 0.20000000
## 107    0.2530073             0.1428571      0.05714286 0.20000000
## 108    0.2530073             0.1428571      0.05714286 0.20000000
## 109    0.2530073             0.1428571      0.05714286 0.20000000
## 110    0.2530073             0.1428571      0.05714286 0.20000000
## 111    0.2530073             0.1428571      0.05714286 0.20000000
## 112    0.2530073             0.1428571      0.05714286 0.20000000
## 113    0.2530073             0.1428571      0.05714286 0.20000000
## 114    0.2530073             0.1428571      0.05714286 0.20000000
## 115    0.2530073             0.1428571      0.05714286 0.20000000
## 116    0.2530073             0.1428571      0.05714286 0.20000000
## 117    0.2530073             0.1428571      0.05714286 0.20000000
## 118    0.2530073             0.1428571      0.05714286 0.20000000
## 119    0.2530073             0.1428571      0.05714286 0.20000000
## 120    0.2530073             0.1428571      0.05714286 0.20000000
## 121    0.6697618             0.0000000      0.50000000 0.50000000
## 122    0.6697618             0.0000000      0.50000000 0.50000000
## 123    0.6697618             0.0000000      0.50000000 0.50000000
## 124    0.6697618             0.0000000      0.50000000 0.50000000
## 125    0.6697618             0.0000000      0.50000000 0.50000000
## 126    0.6697618             0.0000000      0.50000000 0.50000000
## 127    0.6697618             0.0000000      0.50000000 0.50000000
## 128    0.6697618             0.0000000      0.50000000 0.50000000
## 129    0.6697618             0.0000000      0.50000000 0.50000000
## 130    0.6697618             0.0000000      0.50000000 0.50000000
## 131    0.6697618             0.0000000      0.50000000 0.50000000
## 132    0.6697618             0.0000000      0.50000000 0.50000000
## 133    0.6697618             0.0000000      0.50000000 0.50000000
## 134    0.6697618             0.0000000      0.50000000 0.50000000
## 135    0.6697618             0.0000000      0.50000000 0.50000000
## 136    0.6697618             0.0000000      0.50000000 0.50000000
## 137    0.6697618             0.0000000      0.50000000 0.50000000
## 138    0.6697618             0.0000000      0.50000000 0.50000000
## 139    0.6697618             0.0000000      0.50000000 0.50000000
## 140    0.6697618             0.0000000      0.50000000 0.50000000
## 141    0.6697618             0.0000000      0.50000000 0.50000000
## 142    0.6697618             0.0000000      0.50000000 0.50000000
## 143    0.6697618             0.0000000      0.50000000 0.50000000
## 144    0.6697618             0.0000000      0.50000000 0.50000000
## 145    0.6679930             0.4000000      0.10000000 0.50000000
## 146    0.6679930             0.4000000      0.10000000 0.50000000
## 147    0.6679930             0.4000000      0.10000000 0.50000000
## 148    0.6679930             0.4000000      0.10000000 0.50000000
## 149    0.6679930             0.4000000      0.10000000 0.50000000
## 150    0.6679930             0.4000000      0.10000000 0.50000000
## 151    0.6679930             0.4000000      0.10000000 0.50000000
## 152    0.6679930             0.4000000      0.10000000 0.50000000
## 153    0.6679930             0.4000000      0.10000000 0.50000000
## 154    0.6679930             0.4000000      0.10000000 0.50000000
## 155    0.6679930             0.4000000      0.10000000 0.50000000
## 156    0.6679930             0.4000000      0.10000000 0.50000000
## 157    0.6679930             0.4000000      0.10000000 0.50000000
## 158    0.6679930             0.4000000      0.10000000 0.50000000
## 159    0.6679930             0.4000000      0.10000000 0.50000000
## 160    0.6679930             0.4000000      0.10000000 0.50000000
## 161    0.6679930             0.4000000      0.10000000 0.50000000
## 162    0.6679930             0.4000000      0.10000000 0.50000000
## 163    0.6679930             0.4000000      0.10000000 0.50000000
## 164    0.6679930             0.4000000      0.10000000 0.50000000
## 165    0.6679930             0.4000000      0.10000000 0.50000000
## 166    0.6679930             0.4000000      0.10000000 0.50000000
## 167    0.6679930             0.4000000      0.10000000 0.50000000
## 168    0.6679930             0.4000000      0.10000000 0.50000000
## 169    0.8449899             0.0000000      0.63636364 0.63636364
## 170    0.8449899             0.0000000      0.63636364 0.63636364
## 171    0.8449899             0.0000000      0.63636364 0.63636364
## 172    0.8449899             0.0000000      0.63636364 0.63636364
## 173    0.8449899             0.0000000      0.63636364 0.63636364
## 174    0.8449899             0.0000000      0.63636364 0.63636364
## 175    0.8449899             0.0000000      0.63636364 0.63636364
## 176    0.8449899             0.0000000      0.63636364 0.63636364
## 177    0.8449899             0.0000000      0.63636364 0.63636364
## 178    0.8449899             0.0000000      0.63636364 0.63636364
## 179    0.8449899             0.0000000      0.63636364 0.63636364
## 180    0.8449899             0.0000000      0.63636364 0.63636364
## 181    0.8449899             0.0000000      0.63636364 0.63636364
## 182    0.8449899             0.0000000      0.63636364 0.63636364
## 183    0.8449899             0.0000000      0.63636364 0.63636364
## 184    0.8449899             0.0000000      0.63636364 0.63636364
## 185    0.8449899             0.0000000      0.63636364 0.63636364
## 186    0.8449899             0.0000000      0.63636364 0.63636364
## 187    0.8449899             0.0000000      0.63636364 0.63636364
## 188    0.8449899             0.0000000      0.63636364 0.63636364
## 189    0.8449899             0.0000000      0.63636364 0.63636364
## 190    0.8449899             0.0000000      0.63636364 0.63636364
## 191    0.8449899             0.0000000      0.63636364 0.63636364
## 192    0.8449899             0.0000000      0.63636364 0.63636364
## 193    0.0000000             0.0000000      0.00000000 0.00000000
## 194    0.0000000             0.0000000      0.00000000 0.00000000
## 195    0.0000000             0.0000000      0.00000000 0.00000000
## 196    0.0000000             0.0000000      0.00000000 0.00000000
## 197    0.0000000             0.0000000      0.00000000 0.00000000
## 198    0.0000000             0.0000000      0.00000000 0.00000000
## 199    0.0000000             0.0000000      0.00000000 0.00000000
## 200    0.0000000             0.0000000      0.00000000 0.00000000
## 201    0.0000000             0.0000000      0.00000000 0.00000000
## 202    0.0000000             0.0000000      0.00000000 0.00000000
## 203    0.0000000             0.0000000      0.00000000 0.00000000
## 204    0.0000000             0.0000000      0.00000000 0.00000000
## 205    0.0000000             0.0000000      0.00000000 0.00000000
## 206    0.0000000             0.0000000      0.00000000 0.00000000
## 207    0.0000000             0.0000000      0.00000000 0.00000000
## 208    0.0000000             0.0000000      0.00000000 0.00000000
## 209    0.0000000             0.0000000      0.00000000 0.00000000
## 210    0.0000000             0.0000000      0.00000000 0.00000000
## 211    0.0000000             0.0000000      0.00000000 0.00000000
## 212    0.0000000             0.0000000      0.00000000 0.00000000
## 213    0.0000000             0.0000000      0.00000000 0.00000000
## 214    0.0000000             0.0000000      0.00000000 0.00000000
## 215    0.0000000             0.0000000      0.00000000 0.00000000
## 216    0.0000000             0.0000000      0.00000000 0.00000000
## 217    0.4148156             0.0000000      0.12500000 0.12500000
## 218    0.4148156             0.0000000      0.12500000 0.12500000
## 219    0.4148156             0.0000000      0.12500000 0.12500000
## 220    0.4148156             0.0000000      0.12500000 0.12500000
## 221    0.4148156             0.0000000      0.12500000 0.12500000
## 222    0.4148156             0.0000000      0.12500000 0.12500000
## 223    0.4148156             0.0000000      0.12500000 0.12500000
## 224    0.4148156             0.0000000      0.12500000 0.12500000
## 225    0.4148156             0.0000000      0.12500000 0.12500000
## 226    0.4148156             0.0000000      0.12500000 0.12500000
## 227    0.4148156             0.0000000      0.12500000 0.12500000
## 228    0.4148156             0.0000000      0.12500000 0.12500000
## 229    0.4148156             0.0000000      0.12500000 0.12500000
## 230    0.4148156             0.0000000      0.12500000 0.12500000
## 231    0.4148156             0.0000000      0.12500000 0.12500000
## 232    0.4148156             0.0000000      0.12500000 0.12500000
## 233    0.4148156             0.0000000      0.12500000 0.12500000
## 234    0.4148156             0.0000000      0.12500000 0.12500000
## 235    0.4148156             0.0000000      0.12500000 0.12500000
## 236    0.4148156             0.0000000      0.12500000 0.12500000
## 237    0.4148156             0.0000000      0.12500000 0.12500000
## 238    0.4148156             0.0000000      0.12500000 0.12500000
## 239    0.4148156             0.0000000      0.12500000 0.12500000
## 240    0.4148156             0.0000000      0.12500000 0.12500000
## 241    0.2515988             0.0000000      0.23076923 0.23076923
## 242    0.2515988             0.0000000      0.23076923 0.23076923
## 243    0.2515988             0.0000000      0.23076923 0.23076923
## 244    0.2515988             0.0000000      0.23076923 0.23076923
## 245    0.2515988             0.0000000      0.23076923 0.23076923
## 246    0.2515988             0.0000000      0.23076923 0.23076923
## 247    0.2515988             0.0000000      0.23076923 0.23076923
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## 1032   0.5154712             0.1250000      0.05147059 0.17647059
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## 1056   0.2919295             0.0000000      0.14285714 0.14285714
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## 1058   0.4418719             0.0000000      0.45454545 0.45454545
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## 1078   0.4418719             0.0000000      0.45454545 0.45454545
## 1079   0.4418719             0.0000000      0.45454545 0.45454545
## 1080   0.4418719             0.0000000      0.45454545 0.45454545
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## 1098   0.8716887             0.3333333      0.22222222 0.55555556
## 1099   0.8716887             0.3333333      0.22222222 0.55555556
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## 1103   0.8716887             0.3333333      0.22222222 0.55555556
## 1104   0.8716887             0.3333333      0.22222222 0.55555556
## 1105   0.8084387             0.0000000      0.75000000 0.75000000
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## 1200   0.3202752             0.1250000      0.05147059 0.17647059
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## 1218   0.4416686             0.0000000      0.28571429 0.28571429
## 1219   0.4416686             0.0000000      0.28571429 0.28571429
## 1220   0.4416686             0.0000000      0.28571429 0.28571429
## 1221   0.4416686             0.0000000      0.28571429 0.28571429
## 1222   0.4416686             0.0000000      0.28571429 0.28571429
## 1223   0.4416686             0.0000000      0.28571429 0.28571429
## 1224   0.4416686             0.0000000      0.28571429 0.28571429
## 1225   0.3505514             0.1666667      0.11904762 0.28571429
## 1226   0.3505514             0.1666667      0.11904762 0.28571429
## 1227   0.3505514             0.1666667      0.11904762 0.28571429
## 1228   0.3505514             0.1666667      0.11904762 0.28571429
## 1229   0.3505514             0.1666667      0.11904762 0.28571429
## 1230   0.3505514             0.1666667      0.11904762 0.28571429
## 1231   0.3505514             0.1666667      0.11904762 0.28571429
## 1232   0.3505514             0.1666667      0.11904762 0.28571429
## 1233   0.3505514             0.1666667      0.11904762 0.28571429
## 1234   0.3505514             0.1666667      0.11904762 0.28571429
## 1235   0.3505514             0.1666667      0.11904762 0.28571429
## 1236   0.3505514             0.1666667      0.11904762 0.28571429
## 1237   0.3505514             0.1666667      0.11904762 0.28571429
## 1238   0.3505514             0.1666667      0.11904762 0.28571429
## 1239   0.3505514             0.1666667      0.11904762 0.28571429
## 1240   0.3505514             0.1666667      0.11904762 0.28571429
## 1241   0.3505514             0.1666667      0.11904762 0.28571429
## 1242   0.3505514             0.1666667      0.11904762 0.28571429
## 1243   0.3505514             0.1666667      0.11904762 0.28571429
## 1244   0.3505514             0.1666667      0.11904762 0.28571429
## 1245   0.3505514             0.1666667      0.11904762 0.28571429
## 1246   0.3505514             0.1666667      0.11904762 0.28571429
## 1247   0.3505514             0.1666667      0.11904762 0.28571429
## 1248   0.3505514             0.1666667      0.11904762 0.28571429
## 1249   0.5994872             0.3333333      0.16666667 0.50000000
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## 1255   0.5994872             0.3333333      0.16666667 0.50000000
## 1256   0.5994872             0.3333333      0.16666667 0.50000000
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## 1258   0.5994872             0.3333333      0.16666667 0.50000000
## 1259   0.5994872             0.3333333      0.16666667 0.50000000
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## 1261   0.5994872             0.3333333      0.16666667 0.50000000
## 1262   0.5994872             0.3333333      0.16666667 0.50000000
## 1263   0.5994872             0.3333333      0.16666667 0.50000000
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## 1267   0.5994872             0.3333333      0.16666667 0.50000000
## 1268   0.5994872             0.3333333      0.16666667 0.50000000
## 1269   0.5994872             0.3333333      0.16666667 0.50000000
## 1270   0.5994872             0.3333333      0.16666667 0.50000000
## 1271   0.5994872             0.3333333      0.16666667 0.50000000
## 1272   0.5994872             0.3333333      0.16666667 0.50000000
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## 1274   0.7404939             0.0000000      0.45454545 0.45454545
## 1275   0.7404939             0.0000000      0.45454545 0.45454545
## 1276   0.7404939             0.0000000      0.45454545 0.45454545
## 1277   0.7404939             0.0000000      0.45454545 0.45454545
## 1278   0.7404939             0.0000000      0.45454545 0.45454545
## 1279   0.7404939             0.0000000      0.45454545 0.45454545
## 1280   0.7404939             0.0000000      0.45454545 0.45454545
## 1281   0.7404939             0.0000000      0.45454545 0.45454545
## 1282   0.7404939             0.0000000      0.45454545 0.45454545
## 1283   0.7404939             0.0000000      0.45454545 0.45454545
## 1284   0.7404939             0.0000000      0.45454545 0.45454545
## 1285   0.7404939             0.0000000      0.45454545 0.45454545
## 1286   0.7404939             0.0000000      0.45454545 0.45454545
## 1287   0.7404939             0.0000000      0.45454545 0.45454545
## 1288   0.7404939             0.0000000      0.45454545 0.45454545
## 1289   0.7404939             0.0000000      0.45454545 0.45454545
## 1290   0.7404939             0.0000000      0.45454545 0.45454545
## 1291   0.7404939             0.0000000      0.45454545 0.45454545
## 1292   0.7404939             0.0000000      0.45454545 0.45454545
## 1293   0.7404939             0.0000000      0.45454545 0.45454545
## 1294   0.7404939             0.0000000      0.45454545 0.45454545
## 1295   0.7404939             0.0000000      0.45454545 0.45454545
## 1296   0.7404939             0.0000000      0.45454545 0.45454545
## 1297   0.8031107             0.0000000      0.75000000 0.75000000
## 1298   0.8031107             0.0000000      0.75000000 0.75000000
## 1299   0.8031107             0.0000000      0.75000000 0.75000000
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## 1302   0.8031107             0.0000000      0.75000000 0.75000000
## 1303   0.8031107             0.0000000      0.75000000 0.75000000
## 1304   0.8031107             0.0000000      0.75000000 0.75000000
## 1305   0.8031107             0.0000000      0.75000000 0.75000000
## 1306   0.8031107             0.0000000      0.75000000 0.75000000
## 1307   0.8031107             0.0000000      0.75000000 0.75000000
## 1308   0.8031107             0.0000000      0.75000000 0.75000000
## 1309   0.8031107             0.0000000      0.75000000 0.75000000
## 1310   0.8031107             0.0000000      0.75000000 0.75000000
## 1311   0.8031107             0.0000000      0.75000000 0.75000000
## 1312   0.8031107             0.0000000      0.75000000 0.75000000
## 1313   0.8031107             0.0000000      0.75000000 0.75000000
## 1314   0.8031107             0.0000000      0.75000000 0.75000000
## 1315   0.8031107             0.0000000      0.75000000 0.75000000
## 1316   0.8031107             0.0000000      0.75000000 0.75000000
## 1317   0.8031107             0.0000000      0.75000000 0.75000000
## 1318   0.8031107             0.0000000      0.75000000 0.75000000
## 1319   0.8031107             0.0000000      0.75000000 0.75000000
## 1320   0.8031107             0.0000000      0.75000000 0.75000000
## 1321   0.8694784             0.0000000      0.75000000 0.75000000
## 1322   0.8694784             0.0000000      0.75000000 0.75000000
## 1323   0.8694784             0.0000000      0.75000000 0.75000000
## 1324   0.8694784             0.0000000      0.75000000 0.75000000
## 1325   0.8694784             0.0000000      0.75000000 0.75000000
## 1326   0.8694784             0.0000000      0.75000000 0.75000000
## 1327   0.8694784             0.0000000      0.75000000 0.75000000
## 1328   0.8694784             0.0000000      0.75000000 0.75000000
## 1329   0.8694784             0.0000000      0.75000000 0.75000000
## 1330   0.8694784             0.0000000      0.75000000 0.75000000
## 1331   0.8694784             0.0000000      0.75000000 0.75000000
## 1332   0.8694784             0.0000000      0.75000000 0.75000000
## 1333   0.8694784             0.0000000      0.75000000 0.75000000
## 1334   0.8694784             0.0000000      0.75000000 0.75000000
## 1335   0.8694784             0.0000000      0.75000000 0.75000000
## 1336   0.8694784             0.0000000      0.75000000 0.75000000
## 1337   0.8694784             0.0000000      0.75000000 0.75000000
## 1338   0.8694784             0.0000000      0.75000000 0.75000000
## 1339   0.8694784             0.0000000      0.75000000 0.75000000
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## 1341   0.8694784             0.0000000      0.75000000 0.75000000
## 1342   0.8694784             0.0000000      0.75000000 0.75000000
## 1343   0.8694784             0.0000000      0.75000000 0.75000000
## 1344   0.8694784             0.0000000      0.75000000 0.75000000
## 1345   0.0000000             0.0000000      0.00000000 0.00000000
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## 1358   0.0000000             0.0000000      0.00000000 0.00000000
## 1359   0.0000000             0.0000000      0.00000000 0.00000000
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## 1363   0.0000000             0.0000000      0.00000000 0.00000000
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## 1370   0.3469772             0.1250000      0.05147059 0.17647059
## 1371   0.3469772             0.1250000      0.05147059 0.17647059
## 1372   0.3469772             0.1250000      0.05147059 0.17647059
## 1373   0.3469772             0.1250000      0.05147059 0.17647059
## 1374   0.3469772             0.1250000      0.05147059 0.17647059
## 1375   0.3469772             0.1250000      0.05147059 0.17647059
## 1376   0.3469772             0.1250000      0.05147059 0.17647059
## 1377   0.3469772             0.1250000      0.05147059 0.17647059
## 1378   0.3469772             0.1250000      0.05147059 0.17647059
## 1379   0.3469772             0.1250000      0.05147059 0.17647059
## 1380   0.3469772             0.1250000      0.05147059 0.17647059
## 1381   0.3469772             0.1250000      0.05147059 0.17647059
## 1382   0.3469772             0.1250000      0.05147059 0.17647059
## 1383   0.3469772             0.1250000      0.05147059 0.17647059
## 1384   0.3469772             0.1250000      0.05147059 0.17647059
## 1385   0.3469772             0.1250000      0.05147059 0.17647059
## 1386   0.3469772             0.1250000      0.05147059 0.17647059
## 1387   0.3469772             0.1250000      0.05147059 0.17647059
## 1388   0.3469772             0.1250000      0.05147059 0.17647059
## 1389   0.3469772             0.1250000      0.05147059 0.17647059
## 1390   0.3469772             0.1250000      0.05147059 0.17647059
## 1391   0.3469772             0.1250000      0.05147059 0.17647059
## 1392   0.3469772             0.1250000      0.05147059 0.17647059
## 1393   0.4354738             0.1111111      0.00000000 0.11111111
## 1394   0.4354738             0.1111111      0.00000000 0.11111111
## 1395   0.4354738             0.1111111      0.00000000 0.11111111
## 1396   0.4354738             0.1111111      0.00000000 0.11111111
## 1397   0.4354738             0.1111111      0.00000000 0.11111111
## 1398   0.4354738             0.1111111      0.00000000 0.11111111
## 1399   0.4354738             0.1111111      0.00000000 0.11111111
## 1400   0.4354738             0.1111111      0.00000000 0.11111111
## 1401   0.4354738             0.1111111      0.00000000 0.11111111
## 1402   0.4354738             0.1111111      0.00000000 0.11111111
## 1403   0.4354738             0.1111111      0.00000000 0.11111111
## 1404   0.4354738             0.1111111      0.00000000 0.11111111
## 1405   0.4354738             0.1111111      0.00000000 0.11111111
## 1406   0.4354738             0.1111111      0.00000000 0.11111111
## 1407   0.4354738             0.1111111      0.00000000 0.11111111
## 1408   0.4354738             0.1111111      0.00000000 0.11111111
## 1409   0.4354738             0.1111111      0.00000000 0.11111111
## 1410   0.4354738             0.1111111      0.00000000 0.11111111
## 1411   0.4354738             0.1111111      0.00000000 0.11111111
## 1412   0.4354738             0.1111111      0.00000000 0.11111111
## 1413   0.4354738             0.1111111      0.00000000 0.11111111
## 1414   0.4354738             0.1111111      0.00000000 0.11111111
## 1415   0.4354738             0.1111111      0.00000000 0.11111111
## 1416   0.4354738             0.1111111      0.00000000 0.11111111
## 1417   0.3385088             0.0000000      0.20000000 0.20000000
## 1418   0.3385088             0.0000000      0.20000000 0.20000000
## 1419   0.3385088             0.0000000      0.20000000 0.20000000
## 1420   0.3385088             0.0000000      0.20000000 0.20000000
## 1421   0.3385088             0.0000000      0.20000000 0.20000000
## 1422   0.3385088             0.0000000      0.20000000 0.20000000
## 1423   0.3385088             0.0000000      0.20000000 0.20000000
## 1424   0.3385088             0.0000000      0.20000000 0.20000000
## 1425   0.3385088             0.0000000      0.20000000 0.20000000
## 1426   0.3385088             0.0000000      0.20000000 0.20000000
## 1427   0.3385088             0.0000000      0.20000000 0.20000000
## 1428   0.3385088             0.0000000      0.20000000 0.20000000
## 1429   0.3385088             0.0000000      0.20000000 0.20000000
## 1430   0.3385088             0.0000000      0.20000000 0.20000000
## 1431   0.3385088             0.0000000      0.20000000 0.20000000
## 1432   0.3385088             0.0000000      0.20000000 0.20000000
## 1433   0.3385088             0.0000000      0.20000000 0.20000000
## 1434   0.3385088             0.0000000      0.20000000 0.20000000
## 1435   0.3385088             0.0000000      0.20000000 0.20000000
## 1436   0.3385088             0.0000000      0.20000000 0.20000000
## 1437   0.3385088             0.0000000      0.20000000 0.20000000
## 1438   0.3385088             0.0000000      0.20000000 0.20000000
## 1439   0.3385088             0.0000000      0.20000000 0.20000000
## 1440   0.3385088             0.0000000      0.20000000 0.20000000
## 1441   0.5940439             0.3333333      0.26666667 0.60000000
## 1442   0.5940439             0.3333333      0.26666667 0.60000000
## 1443   0.5940439             0.3333333      0.26666667 0.60000000
## 1444   0.5940439             0.3333333      0.26666667 0.60000000
## 1445   0.5940439             0.3333333      0.26666667 0.60000000
## 1446   0.5940439             0.3333333      0.26666667 0.60000000
## 1447   0.5940439             0.3333333      0.26666667 0.60000000
## 1448   0.5940439             0.3333333      0.26666667 0.60000000
## 1449   0.5940439             0.3333333      0.26666667 0.60000000
## 1450   0.5940439             0.3333333      0.26666667 0.60000000
## 1451   0.5940439             0.3333333      0.26666667 0.60000000
## 1452   0.5940439             0.3333333      0.26666667 0.60000000
## 1453   0.5940439             0.3333333      0.26666667 0.60000000
## 1454   0.5940439             0.3333333      0.26666667 0.60000000
## 1455   0.5940439             0.3333333      0.26666667 0.60000000
## 1456   0.5940439             0.3333333      0.26666667 0.60000000
## 1457   0.5940439             0.3333333      0.26666667 0.60000000
## 1458   0.5940439             0.3333333      0.26666667 0.60000000
## 1459   0.5940439             0.3333333      0.26666667 0.60000000
## 1460   0.5940439             0.3333333      0.26666667 0.60000000
## 1461   0.5940439             0.3333333      0.26666667 0.60000000
## 1462   0.5940439             0.3333333      0.26666667 0.60000000
## 1463   0.5940439             0.3333333      0.26666667 0.60000000
## 1464   0.5940439             0.3333333      0.26666667 0.60000000
## 1465   0.8289043             0.3333333      0.22222222 0.55555556
## 1466   0.8289043             0.3333333      0.22222222 0.55555556
## 1467   0.8289043             0.3333333      0.22222222 0.55555556
## 1468   0.8289043             0.3333333      0.22222222 0.55555556
## 1469   0.8289043             0.3333333      0.22222222 0.55555556
## 1470   0.8289043             0.3333333      0.22222222 0.55555556
## 1471   0.8289043             0.3333333      0.22222222 0.55555556
## 1472   0.8289043             0.3333333      0.22222222 0.55555556
## 1473   0.8289043             0.3333333      0.22222222 0.55555556
## 1474   0.8289043             0.3333333      0.22222222 0.55555556
## 1475   0.8289043             0.3333333      0.22222222 0.55555556
## 1476   0.8289043             0.3333333      0.22222222 0.55555556
## 1477   0.8289043             0.3333333      0.22222222 0.55555556
## 1478   0.8289043             0.3333333      0.22222222 0.55555556
## 1479   0.8289043             0.3333333      0.22222222 0.55555556
## 1480   0.8289043             0.3333333      0.22222222 0.55555556
## 1481   0.8289043             0.3333333      0.22222222 0.55555556
## 1482   0.8289043             0.3333333      0.22222222 0.55555556
## 1483   0.8289043             0.3333333      0.22222222 0.55555556
## 1484   0.8289043             0.3333333      0.22222222 0.55555556
## 1485   0.8289043             0.3333333      0.22222222 0.55555556
## 1486   0.8289043             0.3333333      0.22222222 0.55555556
## 1487   0.8289043             0.3333333      0.22222222 0.55555556
## 1488   0.8289043             0.3333333      0.22222222 0.55555556
## 1489   0.7909868             0.0000000      0.77777778 0.77777778
## 1490   0.7909868             0.0000000      0.77777778 0.77777778
## 1491   0.7909868             0.0000000      0.77777778 0.77777778
## 1492   0.7909868             0.0000000      0.77777778 0.77777778
## 1493   0.7909868             0.0000000      0.77777778 0.77777778
## 1494   0.7909868             0.0000000      0.77777778 0.77777778
## 1495   0.7909868             0.0000000      0.77777778 0.77777778
## 1496   0.7909868             0.0000000      0.77777778 0.77777778
## 1497   0.7909868             0.0000000      0.77777778 0.77777778
## 1498   0.7909868             0.0000000      0.77777778 0.77777778
## 1499   0.7909868             0.0000000      0.77777778 0.77777778
## 1500   0.7909868             0.0000000      0.77777778 0.77777778
## 1501   0.7909868             0.0000000      0.77777778 0.77777778
## 1502   0.7909868             0.0000000      0.77777778 0.77777778
## 1503   0.7909868             0.0000000      0.77777778 0.77777778
## 1504   0.7909868             0.0000000      0.77777778 0.77777778
## 1505   0.7909868             0.0000000      0.77777778 0.77777778
## 1506   0.7909868             0.0000000      0.77777778 0.77777778
## 1507   0.7909868             0.0000000      0.77777778 0.77777778
## 1508   0.7909868             0.0000000      0.77777778 0.77777778
## 1509   0.7909868             0.0000000      0.77777778 0.77777778
## 1510   0.7909868             0.0000000      0.77777778 0.77777778
## 1511   0.7909868             0.0000000      0.77777778 0.77777778
## 1512   0.7909868             0.0000000      0.77777778 0.77777778
## 1513   0.9186497             0.0000000      0.75000000 0.75000000
## 1514   0.9186497             0.0000000      0.75000000 0.75000000
## 1515   0.9186497             0.0000000      0.75000000 0.75000000
## 1516   0.9186497             0.0000000      0.75000000 0.75000000
## 1517   0.9186497             0.0000000      0.75000000 0.75000000
## 1518   0.9186497             0.0000000      0.75000000 0.75000000
## 1519   0.9186497             0.0000000      0.75000000 0.75000000
## 1520   0.9186497             0.0000000      0.75000000 0.75000000
## 1521   0.9186497             0.0000000      0.75000000 0.75000000
## 1522   0.9186497             0.0000000      0.75000000 0.75000000
## 1523   0.9186497             0.0000000      0.75000000 0.75000000
## 1524   0.9186497             0.0000000      0.75000000 0.75000000
## 1525   0.9186497             0.0000000      0.75000000 0.75000000
## 1526   0.9186497             0.0000000      0.75000000 0.75000000
## 1527   0.9186497             0.0000000      0.75000000 0.75000000
## 1528   0.9186497             0.0000000      0.75000000 0.75000000
## 1529   0.9186497             0.0000000      0.75000000 0.75000000
## 1530   0.9186497             0.0000000      0.75000000 0.75000000
## 1531   0.9186497             0.0000000      0.75000000 0.75000000
## 1532   0.9186497             0.0000000      0.75000000 0.75000000
## 1533   0.9186497             0.0000000      0.75000000 0.75000000
## 1534   0.9186497             0.0000000      0.75000000 0.75000000
## 1535   0.9186497             0.0000000      0.75000000 0.75000000
## 1536   0.9186497             0.0000000      0.75000000 0.75000000
## 1537   0.0000000             0.0000000      0.00000000 0.00000000
## 1538   0.0000000             0.0000000      0.00000000 0.00000000
## 1539   0.0000000             0.0000000      0.00000000 0.00000000
## 1540   0.0000000             0.0000000      0.00000000 0.00000000
## 1541   0.0000000             0.0000000      0.00000000 0.00000000
## 1542   0.0000000             0.0000000      0.00000000 0.00000000
## 1543   0.0000000             0.0000000      0.00000000 0.00000000
## 1544   0.0000000             0.0000000      0.00000000 0.00000000
## 1545   0.0000000             0.0000000      0.00000000 0.00000000
## 1546   0.0000000             0.0000000      0.00000000 0.00000000
## 1547   0.0000000             0.0000000      0.00000000 0.00000000
## 1548   0.0000000             0.0000000      0.00000000 0.00000000
## 1549   0.0000000             0.0000000      0.00000000 0.00000000
## 1550   0.0000000             0.0000000      0.00000000 0.00000000
## 1551   0.0000000             0.0000000      0.00000000 0.00000000
## 1552   0.0000000             0.0000000      0.00000000 0.00000000
## 1553   0.0000000             0.0000000      0.00000000 0.00000000
## 1554   0.0000000             0.0000000      0.00000000 0.00000000
## 1555   0.0000000             0.0000000      0.00000000 0.00000000
## 1556   0.0000000             0.0000000      0.00000000 0.00000000
## 1557   0.0000000             0.0000000      0.00000000 0.00000000
## 1558   0.0000000             0.0000000      0.00000000 0.00000000
## 1559   0.0000000             0.0000000      0.00000000 0.00000000
## 1560   0.0000000             0.0000000      0.00000000 0.00000000
## 1561   0.2449659             0.1428571      0.05714286 0.20000000
## 1562   0.2449659             0.1428571      0.05714286 0.20000000
## 1563   0.2449659             0.1428571      0.05714286 0.20000000
## 1564   0.2449659             0.1428571      0.05714286 0.20000000
## 1565   0.2449659             0.1428571      0.05714286 0.20000000
## 1566   0.2449659             0.1428571      0.05714286 0.20000000
## 1567   0.2449659             0.1428571      0.05714286 0.20000000
## 1568   0.2449659             0.1428571      0.05714286 0.20000000
## 1569   0.2449659             0.1428571      0.05714286 0.20000000
## 1570   0.2449659             0.1428571      0.05714286 0.20000000
## 1571   0.2449659             0.1428571      0.05714286 0.20000000
## 1572   0.2449659             0.1428571      0.05714286 0.20000000
## 1573   0.2449659             0.1428571      0.05714286 0.20000000
## 1574   0.2449659             0.1428571      0.05714286 0.20000000
## 1575   0.2449659             0.1428571      0.05714286 0.20000000
## 1576   0.2449659             0.1428571      0.05714286 0.20000000
## 1577   0.2449659             0.1428571      0.05714286 0.20000000
## 1578   0.2449659             0.1428571      0.05714286 0.20000000
## 1579   0.2449659             0.1428571      0.05714286 0.20000000
## 1580   0.2449659             0.1428571      0.05714286 0.20000000
## 1581   0.2449659             0.1428571      0.05714286 0.20000000
## 1582   0.2449659             0.1428571      0.05714286 0.20000000
## 1583   0.2449659             0.1428571      0.05714286 0.20000000
## 1584   0.2449659             0.1428571      0.05714286 0.20000000
## 1585   0.4391368             0.1250000      0.05147059 0.17647059
## 1586   0.4391368             0.1250000      0.05147059 0.17647059
## 1587   0.4391368             0.1250000      0.05147059 0.17647059
## 1588   0.4391368             0.1250000      0.05147059 0.17647059
## 1589   0.4391368             0.1250000      0.05147059 0.17647059
## 1590   0.4391368             0.1250000      0.05147059 0.17647059
## 1591   0.4391368             0.1250000      0.05147059 0.17647059
## 1592   0.4391368             0.1250000      0.05147059 0.17647059
## 1593   0.4391368             0.1250000      0.05147059 0.17647059
## 1594   0.4391368             0.1250000      0.05147059 0.17647059
## 1595   0.4391368             0.1250000      0.05147059 0.17647059
## 1596   0.4391368             0.1250000      0.05147059 0.17647059
## 1597   0.4391368             0.1250000      0.05147059 0.17647059
## 1598   0.4391368             0.1250000      0.05147059 0.17647059
## 1599   0.4391368             0.1250000      0.05147059 0.17647059
## 1600   0.4391368             0.1250000      0.05147059 0.17647059
## 1601   0.4391368             0.1250000      0.05147059 0.17647059
## 1602   0.4391368             0.1250000      0.05147059 0.17647059
## 1603   0.4391368             0.1250000      0.05147059 0.17647059
## 1604   0.4391368             0.1250000      0.05147059 0.17647059
## 1605   0.4391368             0.1250000      0.05147059 0.17647059
## 1606   0.4391368             0.1250000      0.05147059 0.17647059
## 1607   0.4391368             0.1250000      0.05147059 0.17647059
## 1608   0.4391368             0.1250000      0.05147059 0.17647059
## 1609   0.3402426             0.1666667      0.00000000 0.16666667
## 1610   0.3402426             0.1666667      0.00000000 0.16666667
## 1611   0.3402426             0.1666667      0.00000000 0.16666667
## 1612   0.3402426             0.1666667      0.00000000 0.16666667
## 1613   0.3402426             0.1666667      0.00000000 0.16666667
## 1614   0.3402426             0.1666667      0.00000000 0.16666667
## 1615   0.3402426             0.1666667      0.00000000 0.16666667
## 1616   0.3402426             0.1666667      0.00000000 0.16666667
## 1617   0.3402426             0.1666667      0.00000000 0.16666667
## 1618   0.3402426             0.1666667      0.00000000 0.16666667
## 1619   0.3402426             0.1666667      0.00000000 0.16666667
## 1620   0.3402426             0.1666667      0.00000000 0.16666667
## 1621   0.3402426             0.1666667      0.00000000 0.16666667
## 1622   0.3402426             0.1666667      0.00000000 0.16666667
## 1623   0.3402426             0.1666667      0.00000000 0.16666667
## 1624   0.3402426             0.1666667      0.00000000 0.16666667
## 1625   0.3402426             0.1666667      0.00000000 0.16666667
## 1626   0.3402426             0.1666667      0.00000000 0.16666667
## 1627   0.3402426             0.1666667      0.00000000 0.16666667
## 1628   0.3402426             0.1666667      0.00000000 0.16666667
## 1629   0.3402426             0.1666667      0.00000000 0.16666667
## 1630   0.3402426             0.1666667      0.00000000 0.16666667
## 1631   0.3402426             0.1666667      0.00000000 0.16666667
## 1632   0.3402426             0.1666667      0.00000000 0.16666667
## 1633   0.6258911             0.6666667      0.11111111 0.77777778
## 1634   0.6258911             0.6666667      0.11111111 0.77777778
## 1635   0.6258911             0.6666667      0.11111111 0.77777778
## 1636   0.6258911             0.6666667      0.11111111 0.77777778
## 1637   0.6258911             0.6666667      0.11111111 0.77777778
## 1638   0.6258911             0.6666667      0.11111111 0.77777778
## 1639   0.6258911             0.6666667      0.11111111 0.77777778
## 1640   0.6258911             0.6666667      0.11111111 0.77777778
## 1641   0.6258911             0.6666667      0.11111111 0.77777778
## 1642   0.6258911             0.6666667      0.11111111 0.77777778
## 1643   0.6258911             0.6666667      0.11111111 0.77777778
## 1644   0.6258911             0.6666667      0.11111111 0.77777778
## 1645   0.6258911             0.6666667      0.11111111 0.77777778
## 1646   0.6258911             0.6666667      0.11111111 0.77777778
## 1647   0.6258911             0.6666667      0.11111111 0.77777778
## 1648   0.6258911             0.6666667      0.11111111 0.77777778
## 1649   0.6258911             0.6666667      0.11111111 0.77777778
## 1650   0.6258911             0.6666667      0.11111111 0.77777778
## 1651   0.6258911             0.6666667      0.11111111 0.77777778
## 1652   0.6258911             0.6666667      0.11111111 0.77777778
## 1653   0.6258911             0.6666667      0.11111111 0.77777778
## 1654   0.6258911             0.6666667      0.11111111 0.77777778
## 1655   0.6258911             0.6666667      0.11111111 0.77777778
## 1656   0.6258911             0.6666667      0.11111111 0.77777778
## 1657   0.8822270             0.6666667      0.08333333 0.75000000
## 1658   0.8822270             0.6666667      0.08333333 0.75000000
## 1659   0.8822270             0.6666667      0.08333333 0.75000000
## 1660   0.8822270             0.6666667      0.08333333 0.75000000
## 1661   0.8822270             0.6666667      0.08333333 0.75000000
## 1662   0.8822270             0.6666667      0.08333333 0.75000000
## 1663   0.8822270             0.6666667      0.08333333 0.75000000
## 1664   0.8822270             0.6666667      0.08333333 0.75000000
## 1665   0.8822270             0.6666667      0.08333333 0.75000000
## 1666   0.8822270             0.6666667      0.08333333 0.75000000
## 1667   0.8822270             0.6666667      0.08333333 0.75000000
## 1668   0.8822270             0.6666667      0.08333333 0.75000000
## 1669   0.8822270             0.6666667      0.08333333 0.75000000
## 1670   0.8822270             0.6666667      0.08333333 0.75000000
## 1671   0.8822270             0.6666667      0.08333333 0.75000000
## 1672   0.8822270             0.6666667      0.08333333 0.75000000
## 1673   0.8822270             0.6666667      0.08333333 0.75000000
## 1674   0.8822270             0.6666667      0.08333333 0.75000000
## 1675   0.8822270             0.6666667      0.08333333 0.75000000
## 1676   0.8822270             0.6666667      0.08333333 0.75000000
## 1677   0.8822270             0.6666667      0.08333333 0.75000000
## 1678   0.8822270             0.6666667      0.08333333 0.75000000
## 1679   0.8822270             0.6666667      0.08333333 0.75000000
## 1680   0.8822270             0.6666667      0.08333333 0.75000000
## 1681   0.5858353             0.0000000      0.71428571 0.71428571
## 1682   0.5858353             0.0000000      0.71428571 0.71428571
## 1683   0.5858353             0.0000000      0.71428571 0.71428571
## 1684   0.5858353             0.0000000      0.71428571 0.71428571
## 1685   0.5858353             0.0000000      0.71428571 0.71428571
## 1686   0.5858353             0.0000000      0.71428571 0.71428571
## 1687   0.5858353             0.0000000      0.71428571 0.71428571
## 1688   0.5858353             0.0000000      0.71428571 0.71428571
## 1689   0.5858353             0.0000000      0.71428571 0.71428571
## 1690   0.5858353             0.0000000      0.71428571 0.71428571
## 1691   0.5858353             0.0000000      0.71428571 0.71428571
## 1692   0.5858353             0.0000000      0.71428571 0.71428571
## 1693   0.5858353             0.0000000      0.71428571 0.71428571
## 1694   0.5858353             0.0000000      0.71428571 0.71428571
## 1695   0.5858353             0.0000000      0.71428571 0.71428571
## 1696   0.5858353             0.0000000      0.71428571 0.71428571
## 1697   0.5858353             0.0000000      0.71428571 0.71428571
## 1698   0.5858353             0.0000000      0.71428571 0.71428571
## 1699   0.5858353             0.0000000      0.71428571 0.71428571
## 1700   0.5858353             0.0000000      0.71428571 0.71428571
## 1701   0.5858353             0.0000000      0.71428571 0.71428571
## 1702   0.5858353             0.0000000      0.71428571 0.71428571
## 1703   0.5858353             0.0000000      0.71428571 0.71428571
## 1704   0.5858353             0.0000000      0.71428571 0.71428571
## 1705   0.5997277             0.0000000      0.66666667 0.66666667
## 1706   0.5997277             0.0000000      0.66666667 0.66666667
## 1707   0.5997277             0.0000000      0.66666667 0.66666667
## 1708   0.5997277             0.0000000      0.66666667 0.66666667
## 1709   0.5997277             0.0000000      0.66666667 0.66666667
## 1710   0.5997277             0.0000000      0.66666667 0.66666667
## 1711   0.5997277             0.0000000      0.66666667 0.66666667
## 1712   0.5997277             0.0000000      0.66666667 0.66666667
## 1713   0.5997277             0.0000000      0.66666667 0.66666667
## 1714   0.5997277             0.0000000      0.66666667 0.66666667
## 1715   0.5997277             0.0000000      0.66666667 0.66666667
## 1716   0.5997277             0.0000000      0.66666667 0.66666667
## 1717   0.5997277             0.0000000      0.66666667 0.66666667
## 1718   0.5997277             0.0000000      0.66666667 0.66666667
## 1719   0.5997277             0.0000000      0.66666667 0.66666667
## 1720   0.5997277             0.0000000      0.66666667 0.66666667
## 1721   0.5997277             0.0000000      0.66666667 0.66666667
## 1722   0.5997277             0.0000000      0.66666667 0.66666667
## 1723   0.5997277             0.0000000      0.66666667 0.66666667
## 1724   0.5997277             0.0000000      0.66666667 0.66666667
## 1725   0.5997277             0.0000000      0.66666667 0.66666667
## 1726   0.5997277             0.0000000      0.66666667 0.66666667
## 1727   0.5997277             0.0000000      0.66666667 0.66666667
## 1728   0.5997277             0.0000000      0.66666667 0.66666667
## 1729   0.0000000             0.0000000      0.00000000 0.00000000
## 1730   0.0000000             0.0000000      0.00000000 0.00000000
## 1731   0.0000000             0.0000000      0.00000000 0.00000000
## 1732   0.0000000             0.0000000      0.00000000 0.00000000
## 1733   0.0000000             0.0000000      0.00000000 0.00000000
## 1734   0.0000000             0.0000000      0.00000000 0.00000000
## 1735   0.0000000             0.0000000      0.00000000 0.00000000
## 1736   0.0000000             0.0000000      0.00000000 0.00000000
## 1737   0.0000000             0.0000000      0.00000000 0.00000000
## 1738   0.0000000             0.0000000      0.00000000 0.00000000
## 1739   0.0000000             0.0000000      0.00000000 0.00000000
## 1740   0.0000000             0.0000000      0.00000000 0.00000000
## 1741   0.0000000             0.0000000      0.00000000 0.00000000
## 1742   0.0000000             0.0000000      0.00000000 0.00000000
## 1743   0.0000000             0.0000000      0.00000000 0.00000000
## 1744   0.0000000             0.0000000      0.00000000 0.00000000
## 1745   0.0000000             0.0000000      0.00000000 0.00000000
## 1746   0.0000000             0.0000000      0.00000000 0.00000000
## 1747   0.0000000             0.0000000      0.00000000 0.00000000
## 1748   0.0000000             0.0000000      0.00000000 0.00000000
## 1749   0.0000000             0.0000000      0.00000000 0.00000000
## 1750   0.0000000             0.0000000      0.00000000 0.00000000
## 1751   0.0000000             0.0000000      0.00000000 0.00000000
## 1752   0.0000000             0.0000000      0.00000000 0.00000000
## 1753   0.3551153             0.0000000      0.05882353 0.05882353
## 1754   0.3551153             0.0000000      0.05882353 0.05882353
## 1755   0.3551153             0.0000000      0.05882353 0.05882353
## 1756   0.3551153             0.0000000      0.05882353 0.05882353
## 1757   0.3551153             0.0000000      0.05882353 0.05882353
## 1758   0.3551153             0.0000000      0.05882353 0.05882353
## 1759   0.3551153             0.0000000      0.05882353 0.05882353
## 1760   0.3551153             0.0000000      0.05882353 0.05882353
## 1761   0.3551153             0.0000000      0.05882353 0.05882353
## 1762   0.3551153             0.0000000      0.05882353 0.05882353
## 1763   0.3551153             0.0000000      0.05882353 0.05882353
## 1764   0.3551153             0.0000000      0.05882353 0.05882353
## 1765   0.3551153             0.0000000      0.05882353 0.05882353
## 1766   0.3551153             0.0000000      0.05882353 0.05882353
## 1767   0.3551153             0.0000000      0.05882353 0.05882353
## 1768   0.3551153             0.0000000      0.05882353 0.05882353
## 1769   0.3551153             0.0000000      0.05882353 0.05882353
## 1770   0.3551153             0.0000000      0.05882353 0.05882353
## 1771   0.3551153             0.0000000      0.05882353 0.05882353
## 1772   0.3551153             0.0000000      0.05882353 0.05882353
## 1773   0.3551153             0.0000000      0.05882353 0.05882353
## 1774   0.3551153             0.0000000      0.05882353 0.05882353
## 1775   0.3551153             0.0000000      0.05882353 0.05882353
## 1776   0.3551153             0.0000000      0.05882353 0.05882353
## 1777   0.5391824             0.1428571      0.10714286 0.25000000
## 1778   0.5391824             0.1428571      0.10714286 0.25000000
## 1779   0.5391824             0.1428571      0.10714286 0.25000000
## 1780   0.5391824             0.1428571      0.10714286 0.25000000
## 1781   0.5391824             0.1428571      0.10714286 0.25000000
## 1782   0.5391824             0.1428571      0.10714286 0.25000000
## 1783   0.5391824             0.1428571      0.10714286 0.25000000
## 1784   0.5391824             0.1428571      0.10714286 0.25000000
## 1785   0.5391824             0.1428571      0.10714286 0.25000000
## 1786   0.5391824             0.1428571      0.10714286 0.25000000
## 1787   0.5391824             0.1428571      0.10714286 0.25000000
## 1788   0.5391824             0.1428571      0.10714286 0.25000000
## 1789   0.5391824             0.1428571      0.10714286 0.25000000
## 1790   0.5391824             0.1428571      0.10714286 0.25000000
## 1791   0.5391824             0.1428571      0.10714286 0.25000000
## 1792   0.5391824             0.1428571      0.10714286 0.25000000
## 1793   0.5391824             0.1428571      0.10714286 0.25000000
## 1794   0.5391824             0.1428571      0.10714286 0.25000000
## 1795   0.5391824             0.1428571      0.10714286 0.25000000
## 1796   0.5391824             0.1428571      0.10714286 0.25000000
## 1797   0.5391824             0.1428571      0.10714286 0.25000000
## 1798   0.5391824             0.1428571      0.10714286 0.25000000
## 1799   0.5391824             0.1428571      0.10714286 0.25000000
## 1800   0.5391824             0.1428571      0.10714286 0.25000000
## 1801   0.3120000             0.0000000      0.14285714 0.14285714
## 1802   0.3120000             0.0000000      0.14285714 0.14285714
## 1803   0.3120000             0.0000000      0.14285714 0.14285714
## 1804   0.3120000             0.0000000      0.14285714 0.14285714
## 1805   0.3120000             0.0000000      0.14285714 0.14285714
## 1806   0.3120000             0.0000000      0.14285714 0.14285714
## 1807   0.3120000             0.0000000      0.14285714 0.14285714
## 1808   0.3120000             0.0000000      0.14285714 0.14285714
## 1809   0.3120000             0.0000000      0.14285714 0.14285714
## 1810   0.3120000             0.0000000      0.14285714 0.14285714
## 1811   0.3120000             0.0000000      0.14285714 0.14285714
## 1812   0.3120000             0.0000000      0.14285714 0.14285714
## 1813   0.3120000             0.0000000      0.14285714 0.14285714
## 1814   0.3120000             0.0000000      0.14285714 0.14285714
## 1815   0.3120000             0.0000000      0.14285714 0.14285714
## 1816   0.3120000             0.0000000      0.14285714 0.14285714
## 1817   0.3120000             0.0000000      0.14285714 0.14285714
## 1818   0.3120000             0.0000000      0.14285714 0.14285714
## 1819   0.3120000             0.0000000      0.14285714 0.14285714
## 1820   0.3120000             0.0000000      0.14285714 0.14285714
## 1821   0.3120000             0.0000000      0.14285714 0.14285714
## 1822   0.3120000             0.0000000      0.14285714 0.14285714
## 1823   0.3120000             0.0000000      0.14285714 0.14285714
## 1824   0.3120000             0.0000000      0.14285714 0.14285714
## 1825   0.5950220             0.3333333      0.30303030 0.63636364
## 1826   0.5950220             0.3333333      0.30303030 0.63636364
## 1827   0.5950220             0.3333333      0.30303030 0.63636364
## 1828   0.5950220             0.3333333      0.30303030 0.63636364
## 1829   0.5950220             0.3333333      0.30303030 0.63636364
## 1830   0.5950220             0.3333333      0.30303030 0.63636364
## 1831   0.5950220             0.3333333      0.30303030 0.63636364
## 1832   0.5950220             0.3333333      0.30303030 0.63636364
## 1833   0.5950220             0.3333333      0.30303030 0.63636364
## 1834   0.5950220             0.3333333      0.30303030 0.63636364
## 1835   0.5950220             0.3333333      0.30303030 0.63636364
## 1836   0.5950220             0.3333333      0.30303030 0.63636364
## 1837   0.5950220             0.3333333      0.30303030 0.63636364
## 1838   0.5950220             0.3333333      0.30303030 0.63636364
## 1839   0.5950220             0.3333333      0.30303030 0.63636364
## 1840   0.5950220             0.3333333      0.30303030 0.63636364
## 1841   0.5950220             0.3333333      0.30303030 0.63636364
## 1842   0.5950220             0.3333333      0.30303030 0.63636364
## 1843   0.5950220             0.3333333      0.30303030 0.63636364
## 1844   0.5950220             0.3333333      0.30303030 0.63636364
## 1845   0.5950220             0.3333333      0.30303030 0.63636364
## 1846   0.5950220             0.3333333      0.30303030 0.63636364
## 1847   0.5950220             0.3333333      0.30303030 0.63636364
## 1848   0.5950220             0.3333333      0.30303030 0.63636364
## 1849   0.8314808             0.3333333      0.30303030 0.63636364
## 1850   0.8314808             0.3333333      0.30303030 0.63636364
## 1851   0.8314808             0.3333333      0.30303030 0.63636364
## 1852   0.8314808             0.3333333      0.30303030 0.63636364
## 1853   0.8314808             0.3333333      0.30303030 0.63636364
## 1854   0.8314808             0.3333333      0.30303030 0.63636364
## 1855   0.8314808             0.3333333      0.30303030 0.63636364
## 1856   0.8314808             0.3333333      0.30303030 0.63636364
## 1857   0.8314808             0.3333333      0.30303030 0.63636364
## 1858   0.8314808             0.3333333      0.30303030 0.63636364
## 1859   0.8314808             0.3333333      0.30303030 0.63636364
## 1860   0.8314808             0.3333333      0.30303030 0.63636364
## 1861   0.8314808             0.3333333      0.30303030 0.63636364
## 1862   0.8314808             0.3333333      0.30303030 0.63636364
## 1863   0.8314808             0.3333333      0.30303030 0.63636364
## 1864   0.8314808             0.3333333      0.30303030 0.63636364
## 1865   0.8314808             0.3333333      0.30303030 0.63636364
## 1866   0.8314808             0.3333333      0.30303030 0.63636364
## 1867   0.8314808             0.3333333      0.30303030 0.63636364
## 1868   0.8314808             0.3333333      0.30303030 0.63636364
## 1869   0.8314808             0.3333333      0.30303030 0.63636364
## 1870   0.8314808             0.3333333      0.30303030 0.63636364
## 1871   0.8314808             0.3333333      0.30303030 0.63636364
## 1872   0.8314808             0.3333333      0.30303030 0.63636364
## 1873   0.8227931             0.0000000      0.77777778 0.77777778
## 1874   0.8227931             0.0000000      0.77777778 0.77777778
## 1875   0.8227931             0.0000000      0.77777778 0.77777778
## 1876   0.8227931             0.0000000      0.77777778 0.77777778
## 1877   0.8227931             0.0000000      0.77777778 0.77777778
## 1878   0.8227931             0.0000000      0.77777778 0.77777778
## 1879   0.8227931             0.0000000      0.77777778 0.77777778
## 1880   0.8227931             0.0000000      0.77777778 0.77777778
## 1881   0.8227931             0.0000000      0.77777778 0.77777778
## 1882   0.8227931             0.0000000      0.77777778 0.77777778
## 1883   0.8227931             0.0000000      0.77777778 0.77777778
## 1884   0.8227931             0.0000000      0.77777778 0.77777778
## 1885   0.8227931             0.0000000      0.77777778 0.77777778
## 1886   0.8227931             0.0000000      0.77777778 0.77777778
## 1887   0.8227931             0.0000000      0.77777778 0.77777778
## 1888   0.8227931             0.0000000      0.77777778 0.77777778
## 1889   0.8227931             0.0000000      0.77777778 0.77777778
## 1890   0.8227931             0.0000000      0.77777778 0.77777778
## 1891   0.8227931             0.0000000      0.77777778 0.77777778
## 1892   0.8227931             0.0000000      0.77777778 0.77777778
## 1893   0.8227931             0.0000000      0.77777778 0.77777778
## 1894   0.8227931             0.0000000      0.77777778 0.77777778
## 1895   0.8227931             0.0000000      0.77777778 0.77777778
## 1896   0.8227931             0.0000000      0.77777778 0.77777778
## 1897   0.9043436             0.0000000      0.77777778 0.77777778
## 1898   0.9043436             0.0000000      0.77777778 0.77777778
## 1899   0.9043436             0.0000000      0.77777778 0.77777778
## 1900   0.9043436             0.0000000      0.77777778 0.77777778
## 1901   0.9043436             0.0000000      0.77777778 0.77777778
## 1902   0.9043436             0.0000000      0.77777778 0.77777778
## 1903   0.9043436             0.0000000      0.77777778 0.77777778
## 1904   0.9043436             0.0000000      0.77777778 0.77777778
## 1905   0.9043436             0.0000000      0.77777778 0.77777778
## 1906   0.9043436             0.0000000      0.77777778 0.77777778
## 1907   0.9043436             0.0000000      0.77777778 0.77777778
## 1908   0.9043436             0.0000000      0.77777778 0.77777778
## 1909   0.9043436             0.0000000      0.77777778 0.77777778
## 1910   0.9043436             0.0000000      0.77777778 0.77777778
## 1911   0.9043436             0.0000000      0.77777778 0.77777778
## 1912   0.9043436             0.0000000      0.77777778 0.77777778
## 1913   0.9043436             0.0000000      0.77777778 0.77777778
## 1914   0.9043436             0.0000000      0.77777778 0.77777778
## 1915   0.9043436             0.0000000      0.77777778 0.77777778
## 1916   0.9043436             0.0000000      0.77777778 0.77777778
## 1917   0.9043436             0.0000000      0.77777778 0.77777778
## 1918   0.9043436             0.0000000      0.77777778 0.77777778
## 1919   0.9043436             0.0000000      0.77777778 0.77777778
## 1920   0.9043436             0.0000000      0.77777778 0.77777778
## 1921   0.0000000             0.0000000      0.00000000 0.00000000
## 1922   0.0000000             0.0000000      0.00000000 0.00000000
## 1923   0.0000000             0.0000000      0.00000000 0.00000000
## 1924   0.0000000             0.0000000      0.00000000 0.00000000
## 1925   0.0000000             0.0000000      0.00000000 0.00000000
## 1926   0.0000000             0.0000000      0.00000000 0.00000000
## 1927   0.0000000             0.0000000      0.00000000 0.00000000
## 1928   0.0000000             0.0000000      0.00000000 0.00000000
## 1929   0.0000000             0.0000000      0.00000000 0.00000000
## 1930   0.0000000             0.0000000      0.00000000 0.00000000
## 1931   0.0000000             0.0000000      0.00000000 0.00000000
## 1932   0.0000000             0.0000000      0.00000000 0.00000000
## 1933   0.0000000             0.0000000      0.00000000 0.00000000
## 1934   0.0000000             0.0000000      0.00000000 0.00000000
## 1935   0.0000000             0.0000000      0.00000000 0.00000000
## 1936   0.0000000             0.0000000      0.00000000 0.00000000
## 1937   0.0000000             0.0000000      0.00000000 0.00000000
## 1938   0.0000000             0.0000000      0.00000000 0.00000000
## 1939   0.0000000             0.0000000      0.00000000 0.00000000
## 1940   0.0000000             0.0000000      0.00000000 0.00000000
## 1941   0.0000000             0.0000000      0.00000000 0.00000000
## 1942   0.0000000             0.0000000      0.00000000 0.00000000
## 1943   0.0000000             0.0000000      0.00000000 0.00000000
## 1944   0.0000000             0.0000000      0.00000000 0.00000000
## 1945   0.3027179             0.0000000      0.14285714 0.14285714
## 1946   0.3027179             0.0000000      0.14285714 0.14285714
## 1947   0.3027179             0.0000000      0.14285714 0.14285714
## 1948   0.3027179             0.0000000      0.14285714 0.14285714
## 1949   0.3027179             0.0000000      0.14285714 0.14285714
## 1950   0.3027179             0.0000000      0.14285714 0.14285714
## 1951   0.3027179             0.0000000      0.14285714 0.14285714
## 1952   0.3027179             0.0000000      0.14285714 0.14285714
## 1953   0.3027179             0.0000000      0.14285714 0.14285714
## 1954   0.3027179             0.0000000      0.14285714 0.14285714
## 1955   0.3027179             0.0000000      0.14285714 0.14285714
## 1956   0.3027179             0.0000000      0.14285714 0.14285714
## 1957   0.3027179             0.0000000      0.14285714 0.14285714
## 1958   0.3027179             0.0000000      0.14285714 0.14285714
## 1959   0.3027179             0.0000000      0.14285714 0.14285714
## 1960   0.3027179             0.0000000      0.14285714 0.14285714
## 1961   0.3027179             0.0000000      0.14285714 0.14285714
## 1962   0.3027179             0.0000000      0.14285714 0.14285714
## 1963   0.3027179             0.0000000      0.14285714 0.14285714
## 1964   0.3027179             0.0000000      0.14285714 0.14285714
## 1965   0.3027179             0.0000000      0.14285714 0.14285714
## 1966   0.3027179             0.0000000      0.14285714 0.14285714
## 1967   0.3027179             0.0000000      0.14285714 0.14285714
## 1968   0.3027179             0.0000000      0.14285714 0.14285714
## 1969   0.3534255             0.0000000      0.14285714 0.14285714
## 1970   0.3534255             0.0000000      0.14285714 0.14285714
## 1971   0.3534255             0.0000000      0.14285714 0.14285714
## 1972   0.3534255             0.0000000      0.14285714 0.14285714
## 1973   0.3534255             0.0000000      0.14285714 0.14285714
## 1974   0.3534255             0.0000000      0.14285714 0.14285714
## 1975   0.3534255             0.0000000      0.14285714 0.14285714
## 1976   0.3534255             0.0000000      0.14285714 0.14285714
## 1977   0.3534255             0.0000000      0.14285714 0.14285714
## 1978   0.3534255             0.0000000      0.14285714 0.14285714
## 1979   0.3534255             0.0000000      0.14285714 0.14285714
## 1980   0.3534255             0.0000000      0.14285714 0.14285714
## 1981   0.3534255             0.0000000      0.14285714 0.14285714
## 1982   0.3534255             0.0000000      0.14285714 0.14285714
## 1983   0.3534255             0.0000000      0.14285714 0.14285714
## 1984   0.3534255             0.0000000      0.14285714 0.14285714
## 1985   0.3534255             0.0000000      0.14285714 0.14285714
## 1986   0.3534255             0.0000000      0.14285714 0.14285714
## 1987   0.3534255             0.0000000      0.14285714 0.14285714
## 1988   0.3534255             0.0000000      0.14285714 0.14285714
## 1989   0.3534255             0.0000000      0.14285714 0.14285714
## 1990   0.3534255             0.0000000      0.14285714 0.14285714
## 1991   0.3534255             0.0000000      0.14285714 0.14285714
## 1992   0.3534255             0.0000000      0.14285714 0.14285714
## 1993   0.5300870             0.0000000      0.33333333 0.33333333
## 1994   0.5300870             0.0000000      0.33333333 0.33333333
## 1995   0.5300870             0.0000000      0.33333333 0.33333333
## 1996   0.5300870             0.0000000      0.33333333 0.33333333
## 1997   0.5300870             0.0000000      0.33333333 0.33333333
## 1998   0.5300870             0.0000000      0.33333333 0.33333333
## 1999   0.5300870             0.0000000      0.33333333 0.33333333
## 2000   0.5300870             0.0000000      0.33333333 0.33333333
## 2001   0.5300870             0.0000000      0.33333333 0.33333333
## 2002   0.5300870             0.0000000      0.33333333 0.33333333
## 2003   0.5300870             0.0000000      0.33333333 0.33333333
## 2004   0.5300870             0.0000000      0.33333333 0.33333333
## 2005   0.5300870             0.0000000      0.33333333 0.33333333
## 2006   0.5300870             0.0000000      0.33333333 0.33333333
## 2007   0.5300870             0.0000000      0.33333333 0.33333333
## 2008   0.5300870             0.0000000      0.33333333 0.33333333
## 2009   0.5300870             0.0000000      0.33333333 0.33333333
## 2010   0.5300870             0.0000000      0.33333333 0.33333333
## 2011   0.5300870             0.0000000      0.33333333 0.33333333
## 2012   0.5300870             0.0000000      0.33333333 0.33333333
## 2013   0.5300870             0.0000000      0.33333333 0.33333333
## 2014   0.5300870             0.0000000      0.33333333 0.33333333
## 2015   0.5300870             0.0000000      0.33333333 0.33333333
## 2016   0.5300870             0.0000000      0.33333333 0.33333333
## 2017   0.5106878             0.2500000      0.25000000 0.50000000
## 2018   0.5106878             0.2500000      0.25000000 0.50000000
## 2019   0.5106878             0.2500000      0.25000000 0.50000000
## 2020   0.5106878             0.2500000      0.25000000 0.50000000
## 2021   0.5106878             0.2500000      0.25000000 0.50000000
## 2022   0.5106878             0.2500000      0.25000000 0.50000000
## 2023   0.5106878             0.2500000      0.25000000 0.50000000
## 2024   0.5106878             0.2500000      0.25000000 0.50000000
## 2025   0.5106878             0.2500000      0.25000000 0.50000000
## 2026   0.5106878             0.2500000      0.25000000 0.50000000
## 2027   0.5106878             0.2500000      0.25000000 0.50000000
## 2028   0.5106878             0.2500000      0.25000000 0.50000000
## 2029   0.5106878             0.2500000      0.25000000 0.50000000
## 2030   0.5106878             0.2500000      0.25000000 0.50000000
## 2031   0.5106878             0.2500000      0.25000000 0.50000000
## 2032   0.5106878             0.2500000      0.25000000 0.50000000
## 2033   0.5106878             0.2500000      0.25000000 0.50000000
## 2034   0.5106878             0.2500000      0.25000000 0.50000000
## 2035   0.5106878             0.2500000      0.25000000 0.50000000
## 2036   0.5106878             0.2500000      0.25000000 0.50000000
## 2037   0.5106878             0.2500000      0.25000000 0.50000000
## 2038   0.5106878             0.2500000      0.25000000 0.50000000
## 2039   0.5106878             0.2500000      0.25000000 0.50000000
## 2040   0.5106878             0.2500000      0.25000000 0.50000000
## 2041   0.7580645             0.5000000      0.25000000 0.75000000
## 2042   0.7580645             0.5000000      0.25000000 0.75000000
## 2043   0.7580645             0.5000000      0.25000000 0.75000000
## 2044   0.7580645             0.5000000      0.25000000 0.75000000
## 2045   0.7580645             0.5000000      0.25000000 0.75000000
## 2046   0.7580645             0.5000000      0.25000000 0.75000000
## 2047   0.7580645             0.5000000      0.25000000 0.75000000
## 2048   0.7580645             0.5000000      0.25000000 0.75000000
## 2049   0.7580645             0.5000000      0.25000000 0.75000000
## 2050   0.7580645             0.5000000      0.25000000 0.75000000
## 2051   0.7580645             0.5000000      0.25000000 0.75000000
## 2052   0.7580645             0.5000000      0.25000000 0.75000000
## 2053   0.7580645             0.5000000      0.25000000 0.75000000
## 2054   0.7580645             0.5000000      0.25000000 0.75000000
## 2055   0.7580645             0.5000000      0.25000000 0.75000000
## 2056   0.7580645             0.5000000      0.25000000 0.75000000
## 2057   0.7580645             0.5000000      0.25000000 0.75000000
## 2058   0.7580645             0.5000000      0.25000000 0.75000000
## 2059   0.7580645             0.5000000      0.25000000 0.75000000
## 2060   0.7580645             0.5000000      0.25000000 0.75000000
## 2061   0.7580645             0.5000000      0.25000000 0.75000000
## 2062   0.7580645             0.5000000      0.25000000 0.75000000
## 2063   0.7580645             0.5000000      0.25000000 0.75000000
## 2064   0.7580645             0.5000000      0.25000000 0.75000000
## 2065   0.8084387             0.0000000      0.40000000 0.40000000
## 2066   0.8084387             0.0000000      0.40000000 0.40000000
## 2067   0.8084387             0.0000000      0.40000000 0.40000000
## 2068   0.8084387             0.0000000      0.40000000 0.40000000
## 2069   0.8084387             0.0000000      0.40000000 0.40000000
## 2070   0.8084387             0.0000000      0.40000000 0.40000000
## 2071   0.8084387             0.0000000      0.40000000 0.40000000
## 2072   0.8084387             0.0000000      0.40000000 0.40000000
## 2073   0.8084387             0.0000000      0.40000000 0.40000000
## 2074   0.8084387             0.0000000      0.40000000 0.40000000
## 2075   0.8084387             0.0000000      0.40000000 0.40000000
## 2076   0.8084387             0.0000000      0.40000000 0.40000000
## 2077   0.8084387             0.0000000      0.40000000 0.40000000
## 2078   0.8084387             0.0000000      0.40000000 0.40000000
## 2079   0.8084387             0.0000000      0.40000000 0.40000000
## 2080   0.8084387             0.0000000      0.40000000 0.40000000
## 2081   0.8084387             0.0000000      0.40000000 0.40000000
## 2082   0.8084387             0.0000000      0.40000000 0.40000000
## 2083   0.8084387             0.0000000      0.40000000 0.40000000
## 2084   0.8084387             0.0000000      0.40000000 0.40000000
## 2085   0.8084387             0.0000000      0.40000000 0.40000000
## 2086   0.8084387             0.0000000      0.40000000 0.40000000
## 2087   0.8084387             0.0000000      0.40000000 0.40000000
## 2088   0.8084387             0.0000000      0.40000000 0.40000000
## 2089   0.8082902             0.5000000      0.31818182 0.81818182
## 2090   0.8082902             0.5000000      0.31818182 0.81818182
## 2091   0.8082902             0.5000000      0.31818182 0.81818182
## 2092   0.8082902             0.5000000      0.31818182 0.81818182
## 2093   0.8082902             0.5000000      0.31818182 0.81818182
## 2094   0.8082902             0.5000000      0.31818182 0.81818182
## 2095   0.8082902             0.5000000      0.31818182 0.81818182
## 2096   0.8082902             0.5000000      0.31818182 0.81818182
## 2097   0.8082902             0.5000000      0.31818182 0.81818182
## 2098   0.8082902             0.5000000      0.31818182 0.81818182
## 2099   0.8082902             0.5000000      0.31818182 0.81818182
## 2100   0.8082902             0.5000000      0.31818182 0.81818182
## 2101   0.8082902             0.5000000      0.31818182 0.81818182
## 2102   0.8082902             0.5000000      0.31818182 0.81818182
## 2103   0.8082902             0.5000000      0.31818182 0.81818182
## 2104   0.8082902             0.5000000      0.31818182 0.81818182
## 2105   0.8082902             0.5000000      0.31818182 0.81818182
## 2106   0.8082902             0.5000000      0.31818182 0.81818182
## 2107   0.8082902             0.5000000      0.31818182 0.81818182
## 2108   0.8082902             0.5000000      0.31818182 0.81818182
## 2109   0.8082902             0.5000000      0.31818182 0.81818182
## 2110   0.8082902             0.5000000      0.31818182 0.81818182
## 2111   0.8082902             0.5000000      0.31818182 0.81818182
## 2112   0.8082902             0.5000000      0.31818182 0.81818182
## 2113   0.0000000             0.0000000      0.00000000 0.00000000
## 2114   0.0000000             0.0000000      0.00000000 0.00000000
## 2115   0.0000000             0.0000000      0.00000000 0.00000000
## 2116   0.0000000             0.0000000      0.00000000 0.00000000
## 2117   0.0000000             0.0000000      0.00000000 0.00000000
## 2118   0.0000000             0.0000000      0.00000000 0.00000000
## 2119   0.0000000             0.0000000      0.00000000 0.00000000
## 2120   0.0000000             0.0000000      0.00000000 0.00000000
## 2121   0.0000000             0.0000000      0.00000000 0.00000000
## 2122   0.0000000             0.0000000      0.00000000 0.00000000
## 2123   0.0000000             0.0000000      0.00000000 0.00000000
## 2124   0.0000000             0.0000000      0.00000000 0.00000000
## 2125   0.0000000             0.0000000      0.00000000 0.00000000
## 2126   0.0000000             0.0000000      0.00000000 0.00000000
## 2127   0.0000000             0.0000000      0.00000000 0.00000000
## 2128   0.0000000             0.0000000      0.00000000 0.00000000
## 2129   0.0000000             0.0000000      0.00000000 0.00000000
## 2130   0.0000000             0.0000000      0.00000000 0.00000000
## 2131   0.0000000             0.0000000      0.00000000 0.00000000
## 2132   0.0000000             0.0000000      0.00000000 0.00000000
## 2133   0.0000000             0.0000000      0.00000000 0.00000000
## 2134   0.0000000             0.0000000      0.00000000 0.00000000
## 2135   0.0000000             0.0000000      0.00000000 0.00000000
## 2136   0.0000000             0.0000000      0.00000000 0.00000000
## 2137   0.4274862             0.1666667      0.16666667 0.33333333
## 2138   0.4274862             0.1666667      0.16666667 0.33333333
## 2139   0.4274862             0.1666667      0.16666667 0.33333333
## 2140   0.4274862             0.1666667      0.16666667 0.33333333
## 2141   0.4274862             0.1666667      0.16666667 0.33333333
## 2142   0.4274862             0.1666667      0.16666667 0.33333333
## 2143   0.4274862             0.1666667      0.16666667 0.33333333
## 2144   0.4274862             0.1666667      0.16666667 0.33333333
## 2145   0.4274862             0.1666667      0.16666667 0.33333333
## 2146   0.4274862             0.1666667      0.16666667 0.33333333
## 2147   0.4274862             0.1666667      0.16666667 0.33333333
## 2148   0.4274862             0.1666667      0.16666667 0.33333333
## 2149   0.4274862             0.1666667      0.16666667 0.33333333
## 2150   0.4274862             0.1666667      0.16666667 0.33333333
## 2151   0.4274862             0.1666667      0.16666667 0.33333333
## 2152   0.4274862             0.1666667      0.16666667 0.33333333
## 2153   0.4274862             0.1666667      0.16666667 0.33333333
## 2154   0.4274862             0.1666667      0.16666667 0.33333333
## 2155   0.4274862             0.1666667      0.16666667 0.33333333
## 2156   0.4274862             0.1666667      0.16666667 0.33333333
## 2157   0.4274862             0.1666667      0.16666667 0.33333333
## 2158   0.4274862             0.1666667      0.16666667 0.33333333
## 2159   0.4274862             0.1666667      0.16666667 0.33333333
## 2160   0.4274862             0.1666667      0.16666667 0.33333333
## 2161   0.1717331             0.0000000      0.09090909 0.09090909
## 2162   0.1717331             0.0000000      0.09090909 0.09090909
## 2163   0.1717331             0.0000000      0.09090909 0.09090909
## 2164   0.1717331             0.0000000      0.09090909 0.09090909
## 2165   0.1717331             0.0000000      0.09090909 0.09090909
## 2166   0.1717331             0.0000000      0.09090909 0.09090909
## 2167   0.1717331             0.0000000      0.09090909 0.09090909
## 2168   0.1717331             0.0000000      0.09090909 0.09090909
## 2169   0.1717331             0.0000000      0.09090909 0.09090909
## 2170   0.1717331             0.0000000      0.09090909 0.09090909
## 2171   0.1717331             0.0000000      0.09090909 0.09090909
## 2172   0.1717331             0.0000000      0.09090909 0.09090909
## 2173   0.1717331             0.0000000      0.09090909 0.09090909
## 2174   0.1717331             0.0000000      0.09090909 0.09090909
## 2175   0.1717331             0.0000000      0.09090909 0.09090909
## 2176   0.1717331             0.0000000      0.09090909 0.09090909
## 2177   0.1717331             0.0000000      0.09090909 0.09090909
## 2178   0.1717331             0.0000000      0.09090909 0.09090909
## 2179   0.1717331             0.0000000      0.09090909 0.09090909
## 2180   0.1717331             0.0000000      0.09090909 0.09090909
## 2181   0.1717331             0.0000000      0.09090909 0.09090909
## 2182   0.1717331             0.0000000      0.09090909 0.09090909
## 2183   0.1717331             0.0000000      0.09090909 0.09090909
## 2184   0.1717331             0.0000000      0.09090909 0.09090909
## 2185   0.4019640             0.0000000      0.33333333 0.33333333
## 2186   0.4019640             0.0000000      0.33333333 0.33333333
## 2187   0.4019640             0.0000000      0.33333333 0.33333333
## 2188   0.4019640             0.0000000      0.33333333 0.33333333
## 2189   0.4019640             0.0000000      0.33333333 0.33333333
## 2190   0.4019640             0.0000000      0.33333333 0.33333333
## 2191   0.4019640             0.0000000      0.33333333 0.33333333
## 2192   0.4019640             0.0000000      0.33333333 0.33333333
## 2193   0.4019640             0.0000000      0.33333333 0.33333333
## 2194   0.4019640             0.0000000      0.33333333 0.33333333
## 2195   0.4019640             0.0000000      0.33333333 0.33333333
## 2196   0.4019640             0.0000000      0.33333333 0.33333333
## 2197   0.4019640             0.0000000      0.33333333 0.33333333
## 2198   0.4019640             0.0000000      0.33333333 0.33333333
## 2199   0.4019640             0.0000000      0.33333333 0.33333333
## 2200   0.4019640             0.0000000      0.33333333 0.33333333
## 2201   0.4019640             0.0000000      0.33333333 0.33333333
## 2202   0.4019640             0.0000000      0.33333333 0.33333333
## 2203   0.4019640             0.0000000      0.33333333 0.33333333
## 2204   0.4019640             0.0000000      0.33333333 0.33333333
## 2205   0.4019640             0.0000000      0.33333333 0.33333333
## 2206   0.4019640             0.0000000      0.33333333 0.33333333
## 2207   0.4019640             0.0000000      0.33333333 0.33333333
## 2208   0.4019640             0.0000000      0.33333333 0.33333333
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## 2220   0.3756846             0.2500000      0.08333333 0.33333333
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## 2222   0.3756846             0.2500000      0.08333333 0.33333333
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## 2227   0.3756846             0.2500000      0.08333333 0.33333333
## 2228   0.3756846             0.2500000      0.08333333 0.33333333
## 2229   0.3756846             0.2500000      0.08333333 0.33333333
## 2230   0.3756846             0.2500000      0.08333333 0.33333333
## 2231   0.3756846             0.2500000      0.08333333 0.33333333
## 2232   0.3756846             0.2500000      0.08333333 0.33333333
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## 2234   0.7278202             0.0000000      0.60000000 0.60000000
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## 2238   0.7278202             0.0000000      0.60000000 0.60000000
## 2239   0.7278202             0.0000000      0.60000000 0.60000000
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## 2241   0.7278202             0.0000000      0.60000000 0.60000000
## 2242   0.7278202             0.0000000      0.60000000 0.60000000
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## 2244   0.7278202             0.0000000      0.60000000 0.60000000
## 2245   0.7278202             0.0000000      0.60000000 0.60000000
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## 2248   0.7278202             0.0000000      0.60000000 0.60000000
## 2249   0.7278202             0.0000000      0.60000000 0.60000000
## 2250   0.7278202             0.0000000      0.60000000 0.60000000
## 2251   0.7278202             0.0000000      0.60000000 0.60000000
## 2252   0.7278202             0.0000000      0.60000000 0.60000000
## 2253   0.7278202             0.0000000      0.60000000 0.60000000
## 2254   0.7278202             0.0000000      0.60000000 0.60000000
## 2255   0.7278202             0.0000000      0.60000000 0.60000000
## 2256   0.7278202             0.0000000      0.60000000 0.60000000
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## 2258   0.8397072             0.0000000      0.40000000 0.40000000
## 2259   0.8397072             0.0000000      0.40000000 0.40000000
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## 2261   0.8397072             0.0000000      0.40000000 0.40000000
## 2262   0.8397072             0.0000000      0.40000000 0.40000000
## 2263   0.8397072             0.0000000      0.40000000 0.40000000
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## 2265   0.8397072             0.0000000      0.40000000 0.40000000
## 2266   0.8397072             0.0000000      0.40000000 0.40000000
## 2267   0.8397072             0.0000000      0.40000000 0.40000000
## 2268   0.8397072             0.0000000      0.40000000 0.40000000
## 2269   0.8397072             0.0000000      0.40000000 0.40000000
## 2270   0.8397072             0.0000000      0.40000000 0.40000000
## 2271   0.8397072             0.0000000      0.40000000 0.40000000
## 2272   0.8397072             0.0000000      0.40000000 0.40000000
## 2273   0.8397072             0.0000000      0.40000000 0.40000000
## 2274   0.8397072             0.0000000      0.40000000 0.40000000
## 2275   0.8397072             0.0000000      0.40000000 0.40000000
## 2276   0.8397072             0.0000000      0.40000000 0.40000000
## 2277   0.8397072             0.0000000      0.40000000 0.40000000
## 2278   0.8397072             0.0000000      0.40000000 0.40000000
## 2279   0.8397072             0.0000000      0.40000000 0.40000000
## 2280   0.8397072             0.0000000      0.40000000 0.40000000
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## 2282   0.7597403             0.5000000      0.27777778 0.77777778
## 2283   0.7597403             0.5000000      0.27777778 0.77777778
## 2284   0.7597403             0.5000000      0.27777778 0.77777778
## 2285   0.7597403             0.5000000      0.27777778 0.77777778
## 2286   0.7597403             0.5000000      0.27777778 0.77777778
## 2287   0.7597403             0.5000000      0.27777778 0.77777778
## 2288   0.7597403             0.5000000      0.27777778 0.77777778
## 2289   0.7597403             0.5000000      0.27777778 0.77777778
## 2290   0.7597403             0.5000000      0.27777778 0.77777778
## 2291   0.7597403             0.5000000      0.27777778 0.77777778
## 2292   0.7597403             0.5000000      0.27777778 0.77777778
## 2293   0.7597403             0.5000000      0.27777778 0.77777778
## 2294   0.7597403             0.5000000      0.27777778 0.77777778
## 2295   0.7597403             0.5000000      0.27777778 0.77777778
## 2296   0.7597403             0.5000000      0.27777778 0.77777778
## 2297   0.7597403             0.5000000      0.27777778 0.77777778
## 2298   0.7597403             0.5000000      0.27777778 0.77777778
## 2299   0.7597403             0.5000000      0.27777778 0.77777778
## 2300   0.7597403             0.5000000      0.27777778 0.77777778
## 2301   0.7597403             0.5000000      0.27777778 0.77777778
## 2302   0.7597403             0.5000000      0.27777778 0.77777778
## 2303   0.7597403             0.5000000      0.27777778 0.77777778
## 2304   0.7597403             0.5000000      0.27777778 0.77777778
## 2305   0.0000000             0.0000000      0.00000000 0.00000000
## 2306   0.0000000             0.0000000      0.00000000 0.00000000
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## 2308   0.0000000             0.0000000      0.00000000 0.00000000
## 2309   0.0000000             0.0000000      0.00000000 0.00000000
## 2310   0.0000000             0.0000000      0.00000000 0.00000000
## 2311   0.0000000             0.0000000      0.00000000 0.00000000
## 2312   0.0000000             0.0000000      0.00000000 0.00000000
## 2313   0.0000000             0.0000000      0.00000000 0.00000000
## 2314   0.0000000             0.0000000      0.00000000 0.00000000
## 2315   0.0000000             0.0000000      0.00000000 0.00000000
## 2316   0.0000000             0.0000000      0.00000000 0.00000000
## 2317   0.0000000             0.0000000      0.00000000 0.00000000
## 2318   0.0000000             0.0000000      0.00000000 0.00000000
## 2319   0.0000000             0.0000000      0.00000000 0.00000000
## 2320   0.0000000             0.0000000      0.00000000 0.00000000
## 2321   0.0000000             0.0000000      0.00000000 0.00000000
## 2322   0.0000000             0.0000000      0.00000000 0.00000000
## 2323   0.0000000             0.0000000      0.00000000 0.00000000
## 2324   0.0000000             0.0000000      0.00000000 0.00000000
## 2325   0.0000000             0.0000000      0.00000000 0.00000000
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## 2327   0.0000000             0.0000000      0.00000000 0.00000000
## 2328   0.0000000             0.0000000      0.00000000 0.00000000
## 2329   0.2390555             0.1666667      0.16666667 0.33333333
## 2330   0.2390555             0.1666667      0.16666667 0.33333333
## 2331   0.2390555             0.1666667      0.16666667 0.33333333
## 2332   0.2390555             0.1666667      0.16666667 0.33333333
## 2333   0.2390555             0.1666667      0.16666667 0.33333333
## 2334   0.2390555             0.1666667      0.16666667 0.33333333
## 2335   0.2390555             0.1666667      0.16666667 0.33333333
## 2336   0.2390555             0.1666667      0.16666667 0.33333333
## 2337   0.2390555             0.1666667      0.16666667 0.33333333
## 2338   0.2390555             0.1666667      0.16666667 0.33333333
## 2339   0.2390555             0.1666667      0.16666667 0.33333333
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## 2342   0.2390555             0.1666667      0.16666667 0.33333333
## 2343   0.2390555             0.1666667      0.16666667 0.33333333
## 2344   0.2390555             0.1666667      0.16666667 0.33333333
## 2345   0.2390555             0.1666667      0.16666667 0.33333333
## 2346   0.2390555             0.1666667      0.16666667 0.33333333
## 2347   0.2390555             0.1666667      0.16666667 0.33333333
## 2348   0.2390555             0.1666667      0.16666667 0.33333333
## 2349   0.2390555             0.1666667      0.16666667 0.33333333
## 2350   0.2390555             0.1666667      0.16666667 0.33333333
## 2351   0.2390555             0.1666667      0.16666667 0.33333333
## 2352   0.2390555             0.1666667      0.16666667 0.33333333
## 2353   0.2484533             0.0000000      0.20000000 0.20000000
## 2354   0.2484533             0.0000000      0.20000000 0.20000000
## 2355   0.2484533             0.0000000      0.20000000 0.20000000
## 2356   0.2484533             0.0000000      0.20000000 0.20000000
## 2357   0.2484533             0.0000000      0.20000000 0.20000000
## 2358   0.2484533             0.0000000      0.20000000 0.20000000
## 2359   0.2484533             0.0000000      0.20000000 0.20000000
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## 2361   0.2484533             0.0000000      0.20000000 0.20000000
## 2362   0.2484533             0.0000000      0.20000000 0.20000000
## 2363   0.2484533             0.0000000      0.20000000 0.20000000
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## 2365   0.2484533             0.0000000      0.20000000 0.20000000
## 2366   0.2484533             0.0000000      0.20000000 0.20000000
## 2367   0.2484533             0.0000000      0.20000000 0.20000000
## 2368   0.2484533             0.0000000      0.20000000 0.20000000
## 2369   0.2484533             0.0000000      0.20000000 0.20000000
## 2370   0.2484533             0.0000000      0.20000000 0.20000000
## 2371   0.2484533             0.0000000      0.20000000 0.20000000
## 2372   0.2484533             0.0000000      0.20000000 0.20000000
## 2373   0.2484533             0.0000000      0.20000000 0.20000000
## 2374   0.2484533             0.0000000      0.20000000 0.20000000
## 2375   0.2484533             0.0000000      0.20000000 0.20000000
## 2376   0.2484533             0.0000000      0.20000000 0.20000000
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## 2378   0.4900944             0.0000000      0.38461538 0.38461538
## 2379   0.4900944             0.0000000      0.38461538 0.38461538
## 2380   0.4900944             0.0000000      0.38461538 0.38461538
## 2381   0.4900944             0.0000000      0.38461538 0.38461538
## 2382   0.4900944             0.0000000      0.38461538 0.38461538
## 2383   0.4900944             0.0000000      0.38461538 0.38461538
## 2384   0.4900944             0.0000000      0.38461538 0.38461538
## 2385   0.4900944             0.0000000      0.38461538 0.38461538
## 2386   0.4900944             0.0000000      0.38461538 0.38461538
## 2387   0.4900944             0.0000000      0.38461538 0.38461538
## 2388   0.4900944             0.0000000      0.38461538 0.38461538
## 2389   0.4900944             0.0000000      0.38461538 0.38461538
## 2390   0.4900944             0.0000000      0.38461538 0.38461538
## 2391   0.4900944             0.0000000      0.38461538 0.38461538
## 2392   0.4900944             0.0000000      0.38461538 0.38461538
## 2393   0.4900944             0.0000000      0.38461538 0.38461538
## 2394   0.4900944             0.0000000      0.38461538 0.38461538
## 2395   0.4900944             0.0000000      0.38461538 0.38461538
## 2396   0.4900944             0.0000000      0.38461538 0.38461538
## 2397   0.4900944             0.0000000      0.38461538 0.38461538
## 2398   0.4900944             0.0000000      0.38461538 0.38461538
## 2399   0.4900944             0.0000000      0.38461538 0.38461538
## 2400   0.4900944             0.0000000      0.38461538 0.38461538
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## 2402   0.4155353             0.2500000      0.20454545 0.45454545
## 2403   0.4155353             0.2500000      0.20454545 0.45454545
## 2404   0.4155353             0.2500000      0.20454545 0.45454545
## 2405   0.4155353             0.2500000      0.20454545 0.45454545
## 2406   0.4155353             0.2500000      0.20454545 0.45454545
## 2407   0.4155353             0.2500000      0.20454545 0.45454545
## 2408   0.4155353             0.2500000      0.20454545 0.45454545
## 2409   0.4155353             0.2500000      0.20454545 0.45454545
## 2410   0.4155353             0.2500000      0.20454545 0.45454545
## 2411   0.4155353             0.2500000      0.20454545 0.45454545
## 2412   0.4155353             0.2500000      0.20454545 0.45454545
## 2413   0.4155353             0.2500000      0.20454545 0.45454545
## 2414   0.4155353             0.2500000      0.20454545 0.45454545
## 2415   0.4155353             0.2500000      0.20454545 0.45454545
## 2416   0.4155353             0.2500000      0.20454545 0.45454545
## 2417   0.4155353             0.2500000      0.20454545 0.45454545
## 2418   0.4155353             0.2500000      0.20454545 0.45454545
## 2419   0.4155353             0.2500000      0.20454545 0.45454545
## 2420   0.4155353             0.2500000      0.20454545 0.45454545
## 2421   0.4155353             0.2500000      0.20454545 0.45454545
## 2422   0.4155353             0.2500000      0.20454545 0.45454545
## 2423   0.4155353             0.2500000      0.20454545 0.45454545
## 2424   0.4155353             0.2500000      0.20454545 0.45454545
## 2425   0.7878675             0.5000000      0.25000000 0.75000000
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## 2448   0.7878675             0.5000000      0.25000000 0.75000000
## 2449   0.7909868             0.0000000      0.45454545 0.45454545
## 2450   0.7909868             0.0000000      0.45454545 0.45454545
## 2451   0.7909868             0.0000000      0.45454545 0.45454545
## 2452   0.7909868             0.0000000      0.45454545 0.45454545
## 2453   0.7909868             0.0000000      0.45454545 0.45454545
## 2454   0.7909868             0.0000000      0.45454545 0.45454545
## 2455   0.7909868             0.0000000      0.45454545 0.45454545
## 2456   0.7909868             0.0000000      0.45454545 0.45454545
## 2457   0.7909868             0.0000000      0.45454545 0.45454545
## 2458   0.7909868             0.0000000      0.45454545 0.45454545
## 2459   0.7909868             0.0000000      0.45454545 0.45454545
## 2460   0.7909868             0.0000000      0.45454545 0.45454545
## 2461   0.7909868             0.0000000      0.45454545 0.45454545
## 2462   0.7909868             0.0000000      0.45454545 0.45454545
## 2463   0.7909868             0.0000000      0.45454545 0.45454545
## 2464   0.7909868             0.0000000      0.45454545 0.45454545
## 2465   0.7909868             0.0000000      0.45454545 0.45454545
## 2466   0.7909868             0.0000000      0.45454545 0.45454545
## 2467   0.7909868             0.0000000      0.45454545 0.45454545
## 2468   0.7909868             0.0000000      0.45454545 0.45454545
## 2469   0.7909868             0.0000000      0.45454545 0.45454545
## 2470   0.7909868             0.0000000      0.45454545 0.45454545
## 2471   0.7909868             0.0000000      0.45454545 0.45454545
## 2472   0.7909868             0.0000000      0.45454545 0.45454545
## 2473   0.8452490             0.5000000      0.27777778 0.77777778
## 2474   0.8452490             0.5000000      0.27777778 0.77777778
## 2475   0.8452490             0.5000000      0.27777778 0.77777778
## 2476   0.8452490             0.5000000      0.27777778 0.77777778
## 2477   0.8452490             0.5000000      0.27777778 0.77777778
## 2478   0.8452490             0.5000000      0.27777778 0.77777778
## 2479   0.8452490             0.5000000      0.27777778 0.77777778
## 2480   0.8452490             0.5000000      0.27777778 0.77777778
## 2481   0.8452490             0.5000000      0.27777778 0.77777778
## 2482   0.8452490             0.5000000      0.27777778 0.77777778
## 2483   0.8452490             0.5000000      0.27777778 0.77777778
## 2484   0.8452490             0.5000000      0.27777778 0.77777778
## 2485   0.8452490             0.5000000      0.27777778 0.77777778
## 2486   0.8452490             0.5000000      0.27777778 0.77777778
## 2487   0.8452490             0.5000000      0.27777778 0.77777778
## 2488   0.8452490             0.5000000      0.27777778 0.77777778
## 2489   0.8452490             0.5000000      0.27777778 0.77777778
## 2490   0.8452490             0.5000000      0.27777778 0.77777778
## 2491   0.8452490             0.5000000      0.27777778 0.77777778
## 2492   0.8452490             0.5000000      0.27777778 0.77777778
## 2493   0.8452490             0.5000000      0.27777778 0.77777778
## 2494   0.8452490             0.5000000      0.27777778 0.77777778
## 2495   0.8452490             0.5000000      0.27777778 0.77777778
## 2496   0.8452490             0.5000000      0.27777778 0.77777778
## 2497   0.0000000             0.0000000      0.00000000 0.00000000
## 2498   0.0000000             0.0000000      0.00000000 0.00000000
## 2499   0.0000000             0.0000000      0.00000000 0.00000000
## 2500   0.0000000             0.0000000      0.00000000 0.00000000
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## 2502   0.0000000             0.0000000      0.00000000 0.00000000
## 2503   0.0000000             0.0000000      0.00000000 0.00000000
## 2504   0.0000000             0.0000000      0.00000000 0.00000000
## 2505   0.0000000             0.0000000      0.00000000 0.00000000
## 2506   0.0000000             0.0000000      0.00000000 0.00000000
## 2507   0.0000000             0.0000000      0.00000000 0.00000000
## 2508   0.0000000             0.0000000      0.00000000 0.00000000
## 2509   0.0000000             0.0000000      0.00000000 0.00000000
## 2510   0.0000000             0.0000000      0.00000000 0.00000000
## 2511   0.0000000             0.0000000      0.00000000 0.00000000
## 2512   0.0000000             0.0000000      0.00000000 0.00000000
## 2513   0.0000000             0.0000000      0.00000000 0.00000000
## 2514   0.0000000             0.0000000      0.00000000 0.00000000
## 2515   0.0000000             0.0000000      0.00000000 0.00000000
## 2516   0.0000000             0.0000000      0.00000000 0.00000000
## 2517   0.0000000             0.0000000      0.00000000 0.00000000
## 2518   0.0000000             0.0000000      0.00000000 0.00000000
## 2519   0.0000000             0.0000000      0.00000000 0.00000000
## 2520   0.0000000             0.0000000      0.00000000 0.00000000
## 2521   0.2704892             0.0000000      0.07692308 0.07692308
## 2522   0.2704892             0.0000000      0.07692308 0.07692308
## 2523   0.2704892             0.0000000      0.07692308 0.07692308
## 2524   0.2704892             0.0000000      0.07692308 0.07692308
## 2525   0.2704892             0.0000000      0.07692308 0.07692308
## 2526   0.2704892             0.0000000      0.07692308 0.07692308
## 2527   0.2704892             0.0000000      0.07692308 0.07692308
## 2528   0.2704892             0.0000000      0.07692308 0.07692308
## 2529   0.2704892             0.0000000      0.07692308 0.07692308
## 2530   0.2704892             0.0000000      0.07692308 0.07692308
## 2531   0.2704892             0.0000000      0.07692308 0.07692308
## 2532   0.2704892             0.0000000      0.07692308 0.07692308
## 2533   0.2704892             0.0000000      0.07692308 0.07692308
## 2534   0.2704892             0.0000000      0.07692308 0.07692308
## 2535   0.2704892             0.0000000      0.07692308 0.07692308
## 2536   0.2704892             0.0000000      0.07692308 0.07692308
## 2537   0.2704892             0.0000000      0.07692308 0.07692308
## 2538   0.2704892             0.0000000      0.07692308 0.07692308
## 2539   0.2704892             0.0000000      0.07692308 0.07692308
## 2540   0.2704892             0.0000000      0.07692308 0.07692308
## 2541   0.2704892             0.0000000      0.07692308 0.07692308
## 2542   0.2704892             0.0000000      0.07692308 0.07692308
## 2543   0.2704892             0.0000000      0.07692308 0.07692308
## 2544   0.2704892             0.0000000      0.07692308 0.07692308
## 2545   0.3470454             0.0000000      0.14285714 0.14285714
## 2546   0.3470454             0.0000000      0.14285714 0.14285714
## 2547   0.3470454             0.0000000      0.14285714 0.14285714
## 2548   0.3470454             0.0000000      0.14285714 0.14285714
## 2549   0.3470454             0.0000000      0.14285714 0.14285714
## 2550   0.3470454             0.0000000      0.14285714 0.14285714
## 2551   0.3470454             0.0000000      0.14285714 0.14285714
## 2552   0.3470454             0.0000000      0.14285714 0.14285714
## 2553   0.3470454             0.0000000      0.14285714 0.14285714
## 2554   0.3470454             0.0000000      0.14285714 0.14285714
## 2555   0.3470454             0.0000000      0.14285714 0.14285714
## 2556   0.3470454             0.0000000      0.14285714 0.14285714
## 2557   0.3470454             0.0000000      0.14285714 0.14285714
## 2558   0.3470454             0.0000000      0.14285714 0.14285714
## 2559   0.3470454             0.0000000      0.14285714 0.14285714
## 2560   0.3470454             0.0000000      0.14285714 0.14285714
## 2561   0.3470454             0.0000000      0.14285714 0.14285714
## 2562   0.3470454             0.0000000      0.14285714 0.14285714
## 2563   0.3470454             0.0000000      0.14285714 0.14285714
## 2564   0.3470454             0.0000000      0.14285714 0.14285714
## 2565   0.3470454             0.0000000      0.14285714 0.14285714
## 2566   0.3470454             0.0000000      0.14285714 0.14285714
## 2567   0.3470454             0.0000000      0.14285714 0.14285714
## 2568   0.3470454             0.0000000      0.14285714 0.14285714
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## 2571   0.1830536             0.2500000      0.15000000 0.40000000
## 2572   0.1830536             0.2500000      0.15000000 0.40000000
## 2573   0.1830536             0.2500000      0.15000000 0.40000000
## 2574   0.1830536             0.2500000      0.15000000 0.40000000
## 2575   0.1830536             0.2500000      0.15000000 0.40000000
## 2576   0.1830536             0.2500000      0.15000000 0.40000000
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## 2578   0.1830536             0.2500000      0.15000000 0.40000000
## 2579   0.1830536             0.2500000      0.15000000 0.40000000
## 2580   0.1830536             0.2500000      0.15000000 0.40000000
## 2581   0.1830536             0.2500000      0.15000000 0.40000000
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## 2584   0.1830536             0.2500000      0.15000000 0.40000000
## 2585   0.1830536             0.2500000      0.15000000 0.40000000
## 2586   0.1830536             0.2500000      0.15000000 0.40000000
## 2587   0.1830536             0.2500000      0.15000000 0.40000000
## 2588   0.1830536             0.2500000      0.15000000 0.40000000
## 2589   0.1830536             0.2500000      0.15000000 0.40000000
## 2590   0.1830536             0.2500000      0.15000000 0.40000000
## 2591   0.1830536             0.2500000      0.15000000 0.40000000
## 2592   0.1830536             0.2500000      0.15000000 0.40000000
## 2593   0.4165868             0.2500000      0.15000000 0.40000000
## 2594   0.4165868             0.2500000      0.15000000 0.40000000
## 2595   0.4165868             0.2500000      0.15000000 0.40000000
## 2596   0.4165868             0.2500000      0.15000000 0.40000000
## 2597   0.4165868             0.2500000      0.15000000 0.40000000
## 2598   0.4165868             0.2500000      0.15000000 0.40000000
## 2599   0.4165868             0.2500000      0.15000000 0.40000000
## 2600   0.4165868             0.2500000      0.15000000 0.40000000
## 2601   0.4165868             0.2500000      0.15000000 0.40000000
## 2602   0.4165868             0.2500000      0.15000000 0.40000000
## 2603   0.4165868             0.2500000      0.15000000 0.40000000
## 2604   0.4165868             0.2500000      0.15000000 0.40000000
## 2605   0.4165868             0.2500000      0.15000000 0.40000000
## 2606   0.4165868             0.2500000      0.15000000 0.40000000
## 2607   0.4165868             0.2500000      0.15000000 0.40000000
## 2608   0.4165868             0.2500000      0.15000000 0.40000000
## 2609   0.4165868             0.2500000      0.15000000 0.40000000
## 2610   0.4165868             0.2500000      0.15000000 0.40000000
## 2611   0.4165868             0.2500000      0.15000000 0.40000000
## 2612   0.4165868             0.2500000      0.15000000 0.40000000
## 2613   0.4165868             0.2500000      0.15000000 0.40000000
## 2614   0.4165868             0.2500000      0.15000000 0.40000000
## 2615   0.4165868             0.2500000      0.15000000 0.40000000
## 2616   0.4165868             0.2500000      0.15000000 0.40000000
## 2617   0.6847345             0.5000000      0.21428571 0.71428571
## 2618   0.6847345             0.5000000      0.21428571 0.71428571
## 2619   0.6847345             0.5000000      0.21428571 0.71428571
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## 2621   0.6847345             0.5000000      0.21428571 0.71428571
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## 2623   0.6847345             0.5000000      0.21428571 0.71428571
## 2624   0.6847345             0.5000000      0.21428571 0.71428571
## 2625   0.6847345             0.5000000      0.21428571 0.71428571
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## 2630   0.6847345             0.5000000      0.21428571 0.71428571
## 2631   0.6847345             0.5000000      0.21428571 0.71428571
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## 2633   0.6847345             0.5000000      0.21428571 0.71428571
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## 2639   0.6847345             0.5000000      0.21428571 0.71428571
## 2640   0.6847345             0.5000000      0.21428571 0.71428571
## 2641   0.6820631             0.3333333      0.22222222 0.55555556
## 2642   0.6820631             0.3333333      0.22222222 0.55555556
## 2643   0.6820631             0.3333333      0.22222222 0.55555556
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## 2648   0.6820631             0.3333333      0.22222222 0.55555556
## 2649   0.6820631             0.3333333      0.22222222 0.55555556
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## 2655   0.6820631             0.3333333      0.22222222 0.55555556
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## 2657   0.6820631             0.3333333      0.22222222 0.55555556
## 2658   0.6820631             0.3333333      0.22222222 0.55555556
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## 2661   0.6820631             0.3333333      0.22222222 0.55555556
## 2662   0.6820631             0.3333333      0.22222222 0.55555556
## 2663   0.6820631             0.3333333      0.22222222 0.55555556
## 2664   0.6820631             0.3333333      0.22222222 0.55555556
## 2665   0.5655391             0.5000000      0.21428571 0.71428571
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## 2677   0.5655391             0.5000000      0.21428571 0.71428571
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## 2679   0.5655391             0.5000000      0.21428571 0.71428571
## 2680   0.5655391             0.5000000      0.21428571 0.71428571
## 2681   0.5655391             0.5000000      0.21428571 0.71428571
## 2682   0.5655391             0.5000000      0.21428571 0.71428571
## 2683   0.5655391             0.5000000      0.21428571 0.71428571
## 2684   0.5655391             0.5000000      0.21428571 0.71428571
## 2685   0.5655391             0.5000000      0.21428571 0.71428571
## 2686   0.5655391             0.5000000      0.21428571 0.71428571
## 2687   0.5655391             0.5000000      0.21428571 0.71428571
## 2688   0.5655391             0.5000000      0.21428571 0.71428571
## 2689   0.0000000             0.0000000      0.00000000 0.00000000
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## 2697   0.0000000             0.0000000      0.00000000 0.00000000
## 2698   0.0000000             0.0000000      0.00000000 0.00000000
## 2699   0.0000000             0.0000000      0.00000000 0.00000000
## 2700   0.0000000             0.0000000      0.00000000 0.00000000
## 2701   0.0000000             0.0000000      0.00000000 0.00000000
## 2702   0.0000000             0.0000000      0.00000000 0.00000000
## 2703   0.0000000             0.0000000      0.00000000 0.00000000
## 2704   0.0000000             0.0000000      0.00000000 0.00000000
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## 2706   0.0000000             0.0000000      0.00000000 0.00000000
## 2707   0.0000000             0.0000000      0.00000000 0.00000000
## 2708   0.0000000             0.0000000      0.00000000 0.00000000
## 2709   0.0000000             0.0000000      0.00000000 0.00000000
## 2710   0.0000000             0.0000000      0.00000000 0.00000000
## 2711   0.0000000             0.0000000      0.00000000 0.00000000
## 2712   0.0000000             0.0000000      0.00000000 0.00000000
## 2713   0.5325091             0.0000000      0.20000000 0.20000000
## 2714   0.5325091             0.0000000      0.20000000 0.20000000
## 2715   0.5325091             0.0000000      0.20000000 0.20000000
## 2716   0.5325091             0.0000000      0.20000000 0.20000000
## 2717   0.5325091             0.0000000      0.20000000 0.20000000
## 2718   0.5325091             0.0000000      0.20000000 0.20000000
## 2719   0.5325091             0.0000000      0.20000000 0.20000000
## 2720   0.5325091             0.0000000      0.20000000 0.20000000
## 2721   0.5325091             0.0000000      0.20000000 0.20000000
## 2722   0.5325091             0.0000000      0.20000000 0.20000000
## 2723   0.5325091             0.0000000      0.20000000 0.20000000
## 2724   0.5325091             0.0000000      0.20000000 0.20000000
## 2725   0.5325091             0.0000000      0.20000000 0.20000000
## 2726   0.5325091             0.0000000      0.20000000 0.20000000
## 2727   0.5325091             0.0000000      0.20000000 0.20000000
## 2728   0.5325091             0.0000000      0.20000000 0.20000000
## 2729   0.5325091             0.0000000      0.20000000 0.20000000
## 2730   0.5325091             0.0000000      0.20000000 0.20000000
## 2731   0.5325091             0.0000000      0.20000000 0.20000000
## 2732   0.5325091             0.0000000      0.20000000 0.20000000
## 2733   0.5325091             0.0000000      0.20000000 0.20000000
## 2734   0.5325091             0.0000000      0.20000000 0.20000000
## 2735   0.5325091             0.0000000      0.20000000 0.20000000
## 2736   0.5325091             0.0000000      0.20000000 0.20000000
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## 2738   0.2827829             0.0000000      0.07692308 0.07692308
## 2739   0.2827829             0.0000000      0.07692308 0.07692308
## 2740   0.2827829             0.0000000      0.07692308 0.07692308
## 2741   0.2827829             0.0000000      0.07692308 0.07692308
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## 2752   0.2827829             0.0000000      0.07692308 0.07692308
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## 2754   0.2827829             0.0000000      0.07692308 0.07692308
## 2755   0.2827829             0.0000000      0.07692308 0.07692308
## 2756   0.2827829             0.0000000      0.07692308 0.07692308
## 2757   0.2827829             0.0000000      0.07692308 0.07692308
## 2758   0.2827829             0.0000000      0.07692308 0.07692308
## 2759   0.2827829             0.0000000      0.07692308 0.07692308
## 2760   0.2827829             0.0000000      0.07692308 0.07692308
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## 2762   0.3693305             0.0000000      0.33333333 0.33333333
## 2763   0.3693305             0.0000000      0.33333333 0.33333333
## 2764   0.3693305             0.0000000      0.33333333 0.33333333
## 2765   0.3693305             0.0000000      0.33333333 0.33333333
## 2766   0.3693305             0.0000000      0.33333333 0.33333333
## 2767   0.3693305             0.0000000      0.33333333 0.33333333
## 2768   0.3693305             0.0000000      0.33333333 0.33333333
## 2769   0.3693305             0.0000000      0.33333333 0.33333333
## 2770   0.3693305             0.0000000      0.33333333 0.33333333
## 2771   0.3693305             0.0000000      0.33333333 0.33333333
## 2772   0.3693305             0.0000000      0.33333333 0.33333333
## 2773   0.3693305             0.0000000      0.33333333 0.33333333
## 2774   0.3693305             0.0000000      0.33333333 0.33333333
## 2775   0.3693305             0.0000000      0.33333333 0.33333333
## 2776   0.3693305             0.0000000      0.33333333 0.33333333
## 2777   0.3693305             0.0000000      0.33333333 0.33333333
## 2778   0.3693305             0.0000000      0.33333333 0.33333333
## 2779   0.3693305             0.0000000      0.33333333 0.33333333
## 2780   0.3693305             0.0000000      0.33333333 0.33333333
## 2781   0.3693305             0.0000000      0.33333333 0.33333333
## 2782   0.3693305             0.0000000      0.33333333 0.33333333
## 2783   0.3693305             0.0000000      0.33333333 0.33333333
## 2784   0.3693305             0.0000000      0.33333333 0.33333333
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## 2787   0.3697479             0.2500000      0.25000000 0.50000000
## 2788   0.3697479             0.2500000      0.25000000 0.50000000
## 2789   0.3697479             0.2500000      0.25000000 0.50000000
## 2790   0.3697479             0.2500000      0.25000000 0.50000000
## 2791   0.3697479             0.2500000      0.25000000 0.50000000
## 2792   0.3697479             0.2500000      0.25000000 0.50000000
## 2793   0.3697479             0.2500000      0.25000000 0.50000000
## 2794   0.3697479             0.2500000      0.25000000 0.50000000
## 2795   0.3697479             0.2500000      0.25000000 0.50000000
## 2796   0.3697479             0.2500000      0.25000000 0.50000000
## 2797   0.3697479             0.2500000      0.25000000 0.50000000
## 2798   0.3697479             0.2500000      0.25000000 0.50000000
## 2799   0.3697479             0.2500000      0.25000000 0.50000000
## 2800   0.3697479             0.2500000      0.25000000 0.50000000
## 2801   0.3697479             0.2500000      0.25000000 0.50000000
## 2802   0.3697479             0.2500000      0.25000000 0.50000000
## 2803   0.3697479             0.2500000      0.25000000 0.50000000
## 2804   0.3697479             0.2500000      0.25000000 0.50000000
## 2805   0.3697479             0.2500000      0.25000000 0.50000000
## 2806   0.3697479             0.2500000      0.25000000 0.50000000
## 2807   0.3697479             0.2500000      0.25000000 0.50000000
## 2808   0.3697479             0.2500000      0.25000000 0.50000000
## 2809   0.7911323             0.5000000      0.30000000 0.80000000
## 2810   0.7911323             0.5000000      0.30000000 0.80000000
## 2811   0.7911323             0.5000000      0.30000000 0.80000000
## 2812   0.7911323             0.5000000      0.30000000 0.80000000
## 2813   0.7911323             0.5000000      0.30000000 0.80000000
## 2814   0.7911323             0.5000000      0.30000000 0.80000000
## 2815   0.7911323             0.5000000      0.30000000 0.80000000
## 2816   0.7911323             0.5000000      0.30000000 0.80000000
## 2817   0.7911323             0.5000000      0.30000000 0.80000000
## 2818   0.7911323             0.5000000      0.30000000 0.80000000
## 2819   0.7911323             0.5000000      0.30000000 0.80000000
## 2820   0.7911323             0.5000000      0.30000000 0.80000000
## 2821   0.7911323             0.5000000      0.30000000 0.80000000
## 2822   0.7911323             0.5000000      0.30000000 0.80000000
## 2823   0.7911323             0.5000000      0.30000000 0.80000000
## 2824   0.7911323             0.5000000      0.30000000 0.80000000
## 2825   0.7911323             0.5000000      0.30000000 0.80000000
## 2826   0.7911323             0.5000000      0.30000000 0.80000000
## 2827   0.7911323             0.5000000      0.30000000 0.80000000
## 2828   0.7911323             0.5000000      0.30000000 0.80000000
## 2829   0.7911323             0.5000000      0.30000000 0.80000000
## 2830   0.7911323             0.5000000      0.30000000 0.80000000
## 2831   0.7911323             0.5000000      0.30000000 0.80000000
## 2832   0.7911323             0.5000000      0.30000000 0.80000000
## 2833   0.8227931             0.0000000      0.45454545 0.45454545
## 2834   0.8227931             0.0000000      0.45454545 0.45454545
## 2835   0.8227931             0.0000000      0.45454545 0.45454545
## 2836   0.8227931             0.0000000      0.45454545 0.45454545
## 2837   0.8227931             0.0000000      0.45454545 0.45454545
## 2838   0.8227931             0.0000000      0.45454545 0.45454545
## 2839   0.8227931             0.0000000      0.45454545 0.45454545
## 2840   0.8227931             0.0000000      0.45454545 0.45454545
## 2841   0.8227931             0.0000000      0.45454545 0.45454545
## 2842   0.8227931             0.0000000      0.45454545 0.45454545
## 2843   0.8227931             0.0000000      0.45454545 0.45454545
## 2844   0.8227931             0.0000000      0.45454545 0.45454545
## 2845   0.8227931             0.0000000      0.45454545 0.45454545
## 2846   0.8227931             0.0000000      0.45454545 0.45454545
## 2847   0.8227931             0.0000000      0.45454545 0.45454545
## 2848   0.8227931             0.0000000      0.45454545 0.45454545
## 2849   0.8227931             0.0000000      0.45454545 0.45454545
## 2850   0.8227931             0.0000000      0.45454545 0.45454545
## 2851   0.8227931             0.0000000      0.45454545 0.45454545
## 2852   0.8227931             0.0000000      0.45454545 0.45454545
## 2853   0.8227931             0.0000000      0.45454545 0.45454545
## 2854   0.8227931             0.0000000      0.45454545 0.45454545
## 2855   0.8227931             0.0000000      0.45454545 0.45454545
## 2856   0.8227931             0.0000000      0.45454545 0.45454545
## 2857   0.8197869             0.5000000      0.30000000 0.80000000
## 2858   0.8197869             0.5000000      0.30000000 0.80000000
## 2859   0.8197869             0.5000000      0.30000000 0.80000000
## 2860   0.8197869             0.5000000      0.30000000 0.80000000
## 2861   0.8197869             0.5000000      0.30000000 0.80000000
## 2862   0.8197869             0.5000000      0.30000000 0.80000000
## 2863   0.8197869             0.5000000      0.30000000 0.80000000
## 2864   0.8197869             0.5000000      0.30000000 0.80000000
## 2865   0.8197869             0.5000000      0.30000000 0.80000000
## 2866   0.8197869             0.5000000      0.30000000 0.80000000
## 2867   0.8197869             0.5000000      0.30000000 0.80000000
## 2868   0.8197869             0.5000000      0.30000000 0.80000000
## 2869   0.8197869             0.5000000      0.30000000 0.80000000
## 2870   0.8197869             0.5000000      0.30000000 0.80000000
## 2871   0.8197869             0.5000000      0.30000000 0.80000000
## 2872   0.8197869             0.5000000      0.30000000 0.80000000
## 2873   0.8197869             0.5000000      0.30000000 0.80000000
## 2874   0.8197869             0.5000000      0.30000000 0.80000000
## 2875   0.8197869             0.5000000      0.30000000 0.80000000
## 2876   0.8197869             0.5000000      0.30000000 0.80000000
## 2877   0.8197869             0.5000000      0.30000000 0.80000000
## 2878   0.8197869             0.5000000      0.30000000 0.80000000
## 2879   0.8197869             0.5000000      0.30000000 0.80000000
## 2880   0.8197869             0.5000000      0.30000000 0.80000000
## 2881   0.0000000             0.0000000      0.00000000 0.00000000
## 2882   0.0000000             0.0000000      0.00000000 0.00000000
## 2883   0.0000000             0.0000000      0.00000000 0.00000000
## 2884   0.0000000             0.0000000      0.00000000 0.00000000
## 2885   0.0000000             0.0000000      0.00000000 0.00000000
## 2886   0.0000000             0.0000000      0.00000000 0.00000000
## 2887   0.0000000             0.0000000      0.00000000 0.00000000
## 2888   0.0000000             0.0000000      0.00000000 0.00000000
## 2889   0.0000000             0.0000000      0.00000000 0.00000000
## 2890   0.0000000             0.0000000      0.00000000 0.00000000
## 2891   0.0000000             0.0000000      0.00000000 0.00000000
## 2892   0.0000000             0.0000000      0.00000000 0.00000000
## 2893   0.0000000             0.0000000      0.00000000 0.00000000
## 2894   0.0000000             0.0000000      0.00000000 0.00000000
## 2895   0.0000000             0.0000000      0.00000000 0.00000000
## 2896   0.0000000             0.0000000      0.00000000 0.00000000
## 2897   0.0000000             0.0000000      0.00000000 0.00000000
## 2898   0.0000000             0.0000000      0.00000000 0.00000000
## 2899   0.0000000             0.0000000      0.00000000 0.00000000
## 2900   0.0000000             0.0000000      0.00000000 0.00000000
## 2901   0.0000000             0.0000000      0.00000000 0.00000000
## 2902   0.0000000             0.0000000      0.00000000 0.00000000
## 2903   0.0000000             0.0000000      0.00000000 0.00000000
## 2904   0.0000000             0.0000000      0.00000000 0.00000000
## 2905   0.2174229             0.1428571      0.05714286 0.20000000
## 2906   0.2174229             0.1428571      0.05714286 0.20000000
## 2907   0.2174229             0.1428571      0.05714286 0.20000000
## 2908   0.2174229             0.1428571      0.05714286 0.20000000
## 2909   0.2174229             0.1428571      0.05714286 0.20000000
## 2910   0.2174229             0.1428571      0.05714286 0.20000000
## 2911   0.2174229             0.1428571      0.05714286 0.20000000
## 2912   0.2174229             0.1428571      0.05714286 0.20000000
## 2913   0.2174229             0.1428571      0.05714286 0.20000000
## 2914   0.2174229             0.1428571      0.05714286 0.20000000
## 2915   0.2174229             0.1428571      0.05714286 0.20000000
## 2916   0.2174229             0.1428571      0.05714286 0.20000000
## 2917   0.2174229             0.1428571      0.05714286 0.20000000
## 2918   0.2174229             0.1428571      0.05714286 0.20000000
## 2919   0.2174229             0.1428571      0.05714286 0.20000000
## 2920   0.2174229             0.1428571      0.05714286 0.20000000
## 2921   0.2174229             0.1428571      0.05714286 0.20000000
## 2922   0.2174229             0.1428571      0.05714286 0.20000000
## 2923   0.2174229             0.1428571      0.05714286 0.20000000
## 2924   0.2174229             0.1428571      0.05714286 0.20000000
## 2925   0.2174229             0.1428571      0.05714286 0.20000000
## 2926   0.2174229             0.1428571      0.05714286 0.20000000
## 2927   0.2174229             0.1428571      0.05714286 0.20000000
## 2928   0.2174229             0.1428571      0.05714286 0.20000000
## 2929   0.2764012             0.2500000      0.00000000 0.25000000
## 2930   0.2764012             0.2500000      0.00000000 0.25000000
## 2931   0.2764012             0.2500000      0.00000000 0.25000000
## 2932   0.2764012             0.2500000      0.00000000 0.25000000
## 2933   0.2764012             0.2500000      0.00000000 0.25000000
## 2934   0.2764012             0.2500000      0.00000000 0.25000000
## 2935   0.2764012             0.2500000      0.00000000 0.25000000
## 2936   0.2764012             0.2500000      0.00000000 0.25000000
## 2937   0.2764012             0.2500000      0.00000000 0.25000000
## 2938   0.2764012             0.2500000      0.00000000 0.25000000
## 2939   0.2764012             0.2500000      0.00000000 0.25000000
## 2940   0.2764012             0.2500000      0.00000000 0.25000000
## 2941   0.2764012             0.2500000      0.00000000 0.25000000
## 2942   0.2764012             0.2500000      0.00000000 0.25000000
## 2943   0.2764012             0.2500000      0.00000000 0.25000000
## 2944   0.2764012             0.2500000      0.00000000 0.25000000
## 2945   0.2764012             0.2500000      0.00000000 0.25000000
## 2946   0.2764012             0.2500000      0.00000000 0.25000000
## 2947   0.2764012             0.2500000      0.00000000 0.25000000
## 2948   0.2764012             0.2500000      0.00000000 0.25000000
## 2949   0.2764012             0.2500000      0.00000000 0.25000000
## 2950   0.2764012             0.2500000      0.00000000 0.25000000
## 2951   0.2764012             0.2500000      0.00000000 0.25000000
## 2952   0.2764012             0.2500000      0.00000000 0.25000000
## 2953   0.5498699             0.0000000      0.60000000 0.60000000
## 2954   0.5498699             0.0000000      0.60000000 0.60000000
## 2955   0.5498699             0.0000000      0.60000000 0.60000000
## 2956   0.5498699             0.0000000      0.60000000 0.60000000
## 2957   0.5498699             0.0000000      0.60000000 0.60000000
## 2958   0.5498699             0.0000000      0.60000000 0.60000000
## 2959   0.5498699             0.0000000      0.60000000 0.60000000
## 2960   0.5498699             0.0000000      0.60000000 0.60000000
## 2961   0.5498699             0.0000000      0.60000000 0.60000000
## 2962   0.5498699             0.0000000      0.60000000 0.60000000
## 2963   0.5498699             0.0000000      0.60000000 0.60000000
## 2964   0.5498699             0.0000000      0.60000000 0.60000000
## 2965   0.5498699             0.0000000      0.60000000 0.60000000
## 2966   0.5498699             0.0000000      0.60000000 0.60000000
## 2967   0.5498699             0.0000000      0.60000000 0.60000000
## 2968   0.5498699             0.0000000      0.60000000 0.60000000
## 2969   0.5498699             0.0000000      0.60000000 0.60000000
## 2970   0.5498699             0.0000000      0.60000000 0.60000000
## 2971   0.5498699             0.0000000      0.60000000 0.60000000
## 2972   0.5498699             0.0000000      0.60000000 0.60000000
## 2973   0.5498699             0.0000000      0.60000000 0.60000000
## 2974   0.5498699             0.0000000      0.60000000 0.60000000
## 2975   0.5498699             0.0000000      0.60000000 0.60000000
## 2976   0.5498699             0.0000000      0.60000000 0.60000000
## 2977   0.3891789             0.0000000      0.33333333 0.33333333
## 2978   0.3891789             0.0000000      0.33333333 0.33333333
## 2979   0.3891789             0.0000000      0.33333333 0.33333333
## 2980   0.3891789             0.0000000      0.33333333 0.33333333
## 2981   0.3891789             0.0000000      0.33333333 0.33333333
## 2982   0.3891789             0.0000000      0.33333333 0.33333333
## 2983   0.3891789             0.0000000      0.33333333 0.33333333
## 2984   0.3891789             0.0000000      0.33333333 0.33333333
## 2985   0.3891789             0.0000000      0.33333333 0.33333333
## 2986   0.3891789             0.0000000      0.33333333 0.33333333
## 2987   0.3891789             0.0000000      0.33333333 0.33333333
## 2988   0.3891789             0.0000000      0.33333333 0.33333333
## 2989   0.3891789             0.0000000      0.33333333 0.33333333
## 2990   0.3891789             0.0000000      0.33333333 0.33333333
## 2991   0.3891789             0.0000000      0.33333333 0.33333333
## 2992   0.3891789             0.0000000      0.33333333 0.33333333
## 2993   0.3891789             0.0000000      0.33333333 0.33333333
## 2994   0.3891789             0.0000000      0.33333333 0.33333333
## 2995   0.3891789             0.0000000      0.33333333 0.33333333
## 2996   0.3891789             0.0000000      0.33333333 0.33333333
## 2997   0.3891789             0.0000000      0.33333333 0.33333333
## 2998   0.3891789             0.0000000      0.33333333 0.33333333
## 2999   0.3891789             0.0000000      0.33333333 0.33333333
## 3000   0.3891789             0.0000000      0.33333333 0.33333333
## 3001   0.6899874             0.0000000      0.33333333 0.33333333
## 3002   0.6899874             0.0000000      0.33333333 0.33333333
## 3003   0.6899874             0.0000000      0.33333333 0.33333333
## 3004   0.6899874             0.0000000      0.33333333 0.33333333
## 3005   0.6899874             0.0000000      0.33333333 0.33333333
## 3006   0.6899874             0.0000000      0.33333333 0.33333333
## 3007   0.6899874             0.0000000      0.33333333 0.33333333
## 3008   0.6899874             0.0000000      0.33333333 0.33333333
## 3009   0.6899874             0.0000000      0.33333333 0.33333333
## 3010   0.6899874             0.0000000      0.33333333 0.33333333
## 3011   0.6899874             0.0000000      0.33333333 0.33333333
## 3012   0.6899874             0.0000000      0.33333333 0.33333333
## 3013   0.6899874             0.0000000      0.33333333 0.33333333
## 3014   0.6899874             0.0000000      0.33333333 0.33333333
## 3015   0.6899874             0.0000000      0.33333333 0.33333333
## 3016   0.6899874             0.0000000      0.33333333 0.33333333
## 3017   0.6899874             0.0000000      0.33333333 0.33333333
## 3018   0.6899874             0.0000000      0.33333333 0.33333333
## 3019   0.6899874             0.0000000      0.33333333 0.33333333
## 3020   0.6899874             0.0000000      0.33333333 0.33333333
## 3021   0.6899874             0.0000000      0.33333333 0.33333333
## 3022   0.6899874             0.0000000      0.33333333 0.33333333
## 3023   0.6899874             0.0000000      0.33333333 0.33333333
## 3024   0.6899874             0.0000000      0.33333333 0.33333333
## 3025   0.8495744             0.5000000      0.27777778 0.77777778
## 3026   0.8495744             0.5000000      0.27777778 0.77777778
## 3027   0.8495744             0.5000000      0.27777778 0.77777778
## 3028   0.8495744             0.5000000      0.27777778 0.77777778
## 3029   0.8495744             0.5000000      0.27777778 0.77777778
## 3030   0.8495744             0.5000000      0.27777778 0.77777778
## 3031   0.8495744             0.5000000      0.27777778 0.77777778
## 3032   0.8495744             0.5000000      0.27777778 0.77777778
## 3033   0.8495744             0.5000000      0.27777778 0.77777778
## 3034   0.8495744             0.5000000      0.27777778 0.77777778
## 3035   0.8495744             0.5000000      0.27777778 0.77777778
## 3036   0.8495744             0.5000000      0.27777778 0.77777778
## 3037   0.8495744             0.5000000      0.27777778 0.77777778
## 3038   0.8495744             0.5000000      0.27777778 0.77777778
## 3039   0.8495744             0.5000000      0.27777778 0.77777778
## 3040   0.8495744             0.5000000      0.27777778 0.77777778
## 3041   0.8495744             0.5000000      0.27777778 0.77777778
## 3042   0.8495744             0.5000000      0.27777778 0.77777778
## 3043   0.8495744             0.5000000      0.27777778 0.77777778
## 3044   0.8495744             0.5000000      0.27777778 0.77777778
## 3045   0.8495744             0.5000000      0.27777778 0.77777778
## 3046   0.8495744             0.5000000      0.27777778 0.77777778
## 3047   0.8495744             0.5000000      0.27777778 0.77777778
## 3048   0.8495744             0.5000000      0.27777778 0.77777778
## 3049   0.7915983             0.0000000      0.28571429 0.28571429
## 3050   0.7915983             0.0000000      0.28571429 0.28571429
## 3051   0.7915983             0.0000000      0.28571429 0.28571429
## 3052   0.7915983             0.0000000      0.28571429 0.28571429
## 3053   0.7915983             0.0000000      0.28571429 0.28571429
## 3054   0.7915983             0.0000000      0.28571429 0.28571429
## 3055   0.7915983             0.0000000      0.28571429 0.28571429
## 3056   0.7915983             0.0000000      0.28571429 0.28571429
## 3057   0.7915983             0.0000000      0.28571429 0.28571429
## 3058   0.7915983             0.0000000      0.28571429 0.28571429
## 3059   0.7915983             0.0000000      0.28571429 0.28571429
## 3060   0.7915983             0.0000000      0.28571429 0.28571429
## 3061   0.7915983             0.0000000      0.28571429 0.28571429
## 3062   0.7915983             0.0000000      0.28571429 0.28571429
## 3063   0.7915983             0.0000000      0.28571429 0.28571429
## 3064   0.7915983             0.0000000      0.28571429 0.28571429
## 3065   0.7915983             0.0000000      0.28571429 0.28571429
## 3066   0.7915983             0.0000000      0.28571429 0.28571429
## 3067   0.7915983             0.0000000      0.28571429 0.28571429
## 3068   0.7915983             0.0000000      0.28571429 0.28571429
## 3069   0.7915983             0.0000000      0.28571429 0.28571429
## 3070   0.7915983             0.0000000      0.28571429 0.28571429
## 3071   0.7915983             0.0000000      0.28571429 0.28571429
## 3072   0.7915983             0.0000000      0.28571429 0.28571429
## 3073   0.0000000             0.0000000      0.00000000 0.00000000
## 3074   0.0000000             0.0000000      0.00000000 0.00000000
## 3075   0.0000000             0.0000000      0.00000000 0.00000000
## 3076   0.0000000             0.0000000      0.00000000 0.00000000
## 3077   0.0000000             0.0000000      0.00000000 0.00000000
## 3078   0.0000000             0.0000000      0.00000000 0.00000000
## 3079   0.0000000             0.0000000      0.00000000 0.00000000
## 3080   0.0000000             0.0000000      0.00000000 0.00000000
## 3081   0.0000000             0.0000000      0.00000000 0.00000000
## 3082   0.0000000             0.0000000      0.00000000 0.00000000
## 3083   0.0000000             0.0000000      0.00000000 0.00000000
## 3084   0.0000000             0.0000000      0.00000000 0.00000000
## 3085   0.0000000             0.0000000      0.00000000 0.00000000
## 3086   0.0000000             0.0000000      0.00000000 0.00000000
## 3087   0.0000000             0.0000000      0.00000000 0.00000000
## 3088   0.0000000             0.0000000      0.00000000 0.00000000
## 3089   0.0000000             0.0000000      0.00000000 0.00000000
## 3090   0.0000000             0.0000000      0.00000000 0.00000000
## 3091   0.0000000             0.0000000      0.00000000 0.00000000
## 3092   0.0000000             0.0000000      0.00000000 0.00000000
## 3093   0.0000000             0.0000000      0.00000000 0.00000000
## 3094   0.0000000             0.0000000      0.00000000 0.00000000
## 3095   0.0000000             0.0000000      0.00000000 0.00000000
## 3096   0.0000000             0.0000000      0.00000000 0.00000000
## 3097   0.4719528             0.1428571      0.10714286 0.25000000
## 3098   0.4719528             0.1428571      0.10714286 0.25000000
## 3099   0.4719528             0.1428571      0.10714286 0.25000000
## 3100   0.4719528             0.1428571      0.10714286 0.25000000
## 3101   0.4719528             0.1428571      0.10714286 0.25000000
## 3102   0.4719528             0.1428571      0.10714286 0.25000000
## 3103   0.4719528             0.1428571      0.10714286 0.25000000
## 3104   0.4719528             0.1428571      0.10714286 0.25000000
## 3105   0.4719528             0.1428571      0.10714286 0.25000000
## 3106   0.4719528             0.1428571      0.10714286 0.25000000
## 3107   0.4719528             0.1428571      0.10714286 0.25000000
## 3108   0.4719528             0.1428571      0.10714286 0.25000000
## 3109   0.4719528             0.1428571      0.10714286 0.25000000
## 3110   0.4719528             0.1428571      0.10714286 0.25000000
## 3111   0.4719528             0.1428571      0.10714286 0.25000000
## 3112   0.4719528             0.1428571      0.10714286 0.25000000
## 3113   0.4719528             0.1428571      0.10714286 0.25000000
## 3114   0.4719528             0.1428571      0.10714286 0.25000000
## 3115   0.4719528             0.1428571      0.10714286 0.25000000
## 3116   0.4719528             0.1428571      0.10714286 0.25000000
## 3117   0.4719528             0.1428571      0.10714286 0.25000000
## 3118   0.4719528             0.1428571      0.10714286 0.25000000
## 3119   0.4719528             0.1428571      0.10714286 0.25000000
## 3120   0.4719528             0.1428571      0.10714286 0.25000000
## 3121   0.2212978             0.0000000      0.23076923 0.23076923
## 3122   0.2212978             0.0000000      0.23076923 0.23076923
## 3123   0.2212978             0.0000000      0.23076923 0.23076923
## 3124   0.2212978             0.0000000      0.23076923 0.23076923
## 3125   0.2212978             0.0000000      0.23076923 0.23076923
## 3126   0.2212978             0.0000000      0.23076923 0.23076923
## 3127   0.2212978             0.0000000      0.23076923 0.23076923
## 3128   0.2212978             0.0000000      0.23076923 0.23076923
## 3129   0.2212978             0.0000000      0.23076923 0.23076923
## 3130   0.2212978             0.0000000      0.23076923 0.23076923
## 3131   0.2212978             0.0000000      0.23076923 0.23076923
## 3132   0.2212978             0.0000000      0.23076923 0.23076923
## 3133   0.2212978             0.0000000      0.23076923 0.23076923
## 3134   0.2212978             0.0000000      0.23076923 0.23076923
## 3135   0.2212978             0.0000000      0.23076923 0.23076923
## 3136   0.2212978             0.0000000      0.23076923 0.23076923
## 3137   0.2212978             0.0000000      0.23076923 0.23076923
## 3138   0.2212978             0.0000000      0.23076923 0.23076923
## 3139   0.2212978             0.0000000      0.23076923 0.23076923
## 3140   0.2212978             0.0000000      0.23076923 0.23076923
## 3141   0.2212978             0.0000000      0.23076923 0.23076923
## 3142   0.2212978             0.0000000      0.23076923 0.23076923
## 3143   0.2212978             0.0000000      0.23076923 0.23076923
## 3144   0.2212978             0.0000000      0.23076923 0.23076923
## 3145   0.6384138             0.0000000      0.60000000 0.60000000
## 3146   0.6384138             0.0000000      0.60000000 0.60000000
## 3147   0.6384138             0.0000000      0.60000000 0.60000000
## 3148   0.6384138             0.0000000      0.60000000 0.60000000
## 3149   0.6384138             0.0000000      0.60000000 0.60000000
## 3150   0.6384138             0.0000000      0.60000000 0.60000000
## 3151   0.6384138             0.0000000      0.60000000 0.60000000
## 3152   0.6384138             0.0000000      0.60000000 0.60000000
## 3153   0.6384138             0.0000000      0.60000000 0.60000000
## 3154   0.6384138             0.0000000      0.60000000 0.60000000
## 3155   0.6384138             0.0000000      0.60000000 0.60000000
## 3156   0.6384138             0.0000000      0.60000000 0.60000000
## 3157   0.6384138             0.0000000      0.60000000 0.60000000
## 3158   0.6384138             0.0000000      0.60000000 0.60000000
## 3159   0.6384138             0.0000000      0.60000000 0.60000000
## 3160   0.6384138             0.0000000      0.60000000 0.60000000
## 3161   0.6384138             0.0000000      0.60000000 0.60000000
## 3162   0.6384138             0.0000000      0.60000000 0.60000000
## 3163   0.6384138             0.0000000      0.60000000 0.60000000
## 3164   0.6384138             0.0000000      0.60000000 0.60000000
## 3165   0.6384138             0.0000000      0.60000000 0.60000000
## 3166   0.6384138             0.0000000      0.60000000 0.60000000
## 3167   0.6384138             0.0000000      0.60000000 0.60000000
## 3168   0.6384138             0.0000000      0.60000000 0.60000000
## 3169   0.5259003             0.2500000      0.08333333 0.33333333
## 3170   0.5259003             0.2500000      0.08333333 0.33333333
## 3171   0.5259003             0.2500000      0.08333333 0.33333333
## 3172   0.5259003             0.2500000      0.08333333 0.33333333
## 3173   0.5259003             0.2500000      0.08333333 0.33333333
## 3174   0.5259003             0.2500000      0.08333333 0.33333333
## 3175   0.5259003             0.2500000      0.08333333 0.33333333
## 3176   0.5259003             0.2500000      0.08333333 0.33333333
## 3177   0.5259003             0.2500000      0.08333333 0.33333333
## 3178   0.5259003             0.2500000      0.08333333 0.33333333
## 3179   0.5259003             0.2500000      0.08333333 0.33333333
## 3180   0.5259003             0.2500000      0.08333333 0.33333333
## 3181   0.5259003             0.2500000      0.08333333 0.33333333
## 3182   0.5259003             0.2500000      0.08333333 0.33333333
## 3183   0.5259003             0.2500000      0.08333333 0.33333333
## 3184   0.5259003             0.2500000      0.08333333 0.33333333
## 3185   0.5259003             0.2500000      0.08333333 0.33333333
## 3186   0.5259003             0.2500000      0.08333333 0.33333333
## 3187   0.5259003             0.2500000      0.08333333 0.33333333
## 3188   0.5259003             0.2500000      0.08333333 0.33333333
## 3189   0.5259003             0.2500000      0.08333333 0.33333333
## 3190   0.5259003             0.2500000      0.08333333 0.33333333
## 3191   0.5259003             0.2500000      0.08333333 0.33333333
## 3192   0.5259003             0.2500000      0.08333333 0.33333333
## 3193   0.7065821             0.0000000      0.45454545 0.45454545
## 3194   0.7065821             0.0000000      0.45454545 0.45454545
## 3195   0.7065821             0.0000000      0.45454545 0.45454545
## 3196   0.7065821             0.0000000      0.45454545 0.45454545
## 3197   0.7065821             0.0000000      0.45454545 0.45454545
## 3198   0.7065821             0.0000000      0.45454545 0.45454545
## 3199   0.7065821             0.0000000      0.45454545 0.45454545
## 3200   0.7065821             0.0000000      0.45454545 0.45454545
## 3201   0.7065821             0.0000000      0.45454545 0.45454545
## 3202   0.7065821             0.0000000      0.45454545 0.45454545
## 3203   0.7065821             0.0000000      0.45454545 0.45454545
## 3204   0.7065821             0.0000000      0.45454545 0.45454545
## 3205   0.7065821             0.0000000      0.45454545 0.45454545
## 3206   0.7065821             0.0000000      0.45454545 0.45454545
## 3207   0.7065821             0.0000000      0.45454545 0.45454545
## 3208   0.7065821             0.0000000      0.45454545 0.45454545
## 3209   0.7065821             0.0000000      0.45454545 0.45454545
## 3210   0.7065821             0.0000000      0.45454545 0.45454545
## 3211   0.7065821             0.0000000      0.45454545 0.45454545
## 3212   0.7065821             0.0000000      0.45454545 0.45454545
## 3213   0.7065821             0.0000000      0.45454545 0.45454545
## 3214   0.7065821             0.0000000      0.45454545 0.45454545
## 3215   0.7065821             0.0000000      0.45454545 0.45454545
## 3216   0.7065821             0.0000000      0.45454545 0.45454545
## 3217   0.7709188             0.0000000      0.55555556 0.55555556
## 3218   0.7709188             0.0000000      0.55555556 0.55555556
## 3219   0.7709188             0.0000000      0.55555556 0.55555556
## 3220   0.7709188             0.0000000      0.55555556 0.55555556
## 3221   0.7709188             0.0000000      0.55555556 0.55555556
## 3222   0.7709188             0.0000000      0.55555556 0.55555556
## 3223   0.7709188             0.0000000      0.55555556 0.55555556
## 3224   0.7709188             0.0000000      0.55555556 0.55555556
## 3225   0.7709188             0.0000000      0.55555556 0.55555556
##      metaecosystem_richness total_metaecosystem_bioarea_mm2
## 1                        11                        96.92197
## 2                        11                        96.92197
## 3                        11                        96.92197
## 4                        11                        96.92197
## 5                        11                        96.92197
## 6                        11                        96.92197
## 7                        11                        96.92197
## 8                        11                        96.92197
## 9                        11                        96.92197
## 10                       11                        96.92197
## 11                       11                        96.92197
## 12                       11                        96.92197
## 13                       11                        96.92197
## 14                       11                        96.92197
## 15                       11                        96.92197
## 16                       11                        96.92197
## 17                       11                        96.92197
## 18                       11                        96.92197
## 19                       11                        96.92197
## 20                       11                        96.92197
## 21                       11                        96.92197
## 22                       11                        96.92197
## 23                       11                        96.92197
## 24                       11                        96.92197
## 25                        9                       152.90836
## 26                        9                       152.90836
## 27                        9                       152.90836
## 28                        9                       152.90836
## 29                        9                       152.90836
## 30                        9                       152.90836
## 31                        9                       152.90836
## 32                        9                       152.90836
## 33                        9                       152.90836
## 34                        9                       152.90836
## 35                        9                       152.90836
## 36                        9                       152.90836
## 37                        9                       152.90836
## 38                        9                       152.90836
## 39                        9                       152.90836
## 40                        9                       152.90836
## 41                        9                       152.90836
## 42                        9                       152.90836
## 43                        9                       152.90836
## 44                        9                       152.90836
## 45                        9                       152.90836
## 46                        9                       152.90836
## 47                        9                       152.90836
## 48                        9                       152.90836
## 49                        9                       163.09305
## 50                        9                       163.09305
## 51                        9                       163.09305
## 52                        9                       163.09305
## 53                        9                       163.09305
## 54                        9                       163.09305
## 55                        9                       163.09305
## 56                        9                       163.09305
## 57                        9                       163.09305
## 58                        9                       163.09305
## 59                        9                       163.09305
## 60                        9                       163.09305
## 61                        9                       163.09305
## 62                        9                       163.09305
## 63                        9                       163.09305
## 64                        9                       163.09305
## 65                        9                       163.09305
## 66                        9                       163.09305
## 67                        9                       163.09305
## 68                        9                       163.09305
## 69                        9                       163.09305
## 70                        9                       163.09305
## 71                        9                       163.09305
## 72                        9                       163.09305
## 73                        8                       182.03030
## 74                        8                       182.03030
## 75                        8                       182.03030
## 76                        8                       182.03030
## 77                        8                       182.03030
## 78                        8                       182.03030
## 79                        8                       182.03030
## 80                        8                       182.03030
## 81                        8                       182.03030
## 82                        8                       182.03030
## 83                        8                       182.03030
## 84                        8                       182.03030
## 85                        8                       182.03030
## 86                        8                       182.03030
## 87                        8                       182.03030
## 88                        8                       182.03030
## 89                        8                       182.03030
## 90                        8                       182.03030
## 91                        8                       182.03030
## 92                        8                       182.03030
## 93                        8                       182.03030
## 94                        8                       182.03030
## 95                        8                       182.03030
## 96                        8                       182.03030
## 97                        9                       140.28580
## 98                        9                       140.28580
## 99                        9                       140.28580
## 100                       9                       140.28580
## 101                       9                       140.28580
## 102                       9                       140.28580
## 103                       9                       140.28580
## 104                       9                       140.28580
## 105                       9                       140.28580
## 106                       9                       140.28580
## 107                       9                       140.28580
## 108                       9                       140.28580
## 109                       9                       140.28580
## 110                       9                       140.28580
## 111                       9                       140.28580
## 112                       9                       140.28580
## 113                       9                       140.28580
## 114                       9                       140.28580
## 115                       9                       140.28580
## 116                       9                       140.28580
## 117                       9                       140.28580
## 118                       9                       140.28580
## 119                       9                       140.28580
## 120                       9                       140.28580
## 121                       6                       117.28324
## 122                       6                       117.28324
## 123                       6                       117.28324
## 124                       6                       117.28324
## 125                       6                       117.28324
## 126                       6                       117.28324
## 127                       6                       117.28324
## 128                       6                       117.28324
## 129                       6                       117.28324
## 130                       6                       117.28324
## 131                       6                       117.28324
## 132                       6                       117.28324
## 133                       6                       117.28324
## 134                       6                       117.28324
## 135                       6                       117.28324
## 136                       6                       117.28324
## 137                       6                       117.28324
## 138                       6                       117.28324
## 139                       6                       117.28324
## 140                       6                       117.28324
## 141                       6                       117.28324
## 142                       6                       117.28324
## 143                       6                       117.28324
## 144                       6                       117.28324
## 145                       9                       103.80974
## 146                       9                       103.80974
## 147                       9                       103.80974
## 148                       9                       103.80974
## 149                       9                       103.80974
## 150                       9                       103.80974
## 151                       9                       103.80974
## 152                       9                       103.80974
## 153                       9                       103.80974
## 154                       9                       103.80974
## 155                       9                       103.80974
## 156                       9                       103.80974
## 157                       9                       103.80974
## 158                       9                       103.80974
## 159                       9                       103.80974
## 160                       9                       103.80974
## 161                       9                       103.80974
## 162                       9                       103.80974
## 163                       9                       103.80974
## 164                       9                       103.80974
## 165                       9                       103.80974
## 166                       9                       103.80974
## 167                       9                       103.80974
## 168                       9                       103.80974
## 169                       9                        92.60172
## 170                       9                        92.60172
## 171                       9                        92.60172
## 172                       9                        92.60172
## 173                       9                        92.60172
## 174                       9                        92.60172
## 175                       9                        92.60172
## 176                       9                        92.60172
## 177                       9                        92.60172
## 178                       9                        92.60172
## 179                       9                        92.60172
## 180                       9                        92.60172
## 181                       9                        92.60172
## 182                       9                        92.60172
## 183                       9                        92.60172
## 184                       9                        92.60172
## 185                       9                        92.60172
## 186                       9                        92.60172
## 187                       9                        92.60172
## 188                       9                        92.60172
## 189                       9                        92.60172
## 190                       9                        92.60172
## 191                       9                        92.60172
## 192                       9                        92.60172
## 193                      11                        96.92197
## 194                      11                        96.92197
## 195                      11                        96.92197
## 196                      11                        96.92197
## 197                      11                        96.92197
## 198                      11                        96.92197
## 199                      11                        96.92197
## 200                      11                        96.92197
## 201                      11                        96.92197
## 202                      11                        96.92197
## 203                      11                        96.92197
## 204                      11                        96.92197
## 205                      11                        96.92197
## 206                      11                        96.92197
## 207                      11                        96.92197
## 208                      11                        96.92197
## 209                      11                        96.92197
## 210                      11                        96.92197
## 211                      11                        96.92197
## 212                      11                        96.92197
## 213                      11                        96.92197
## 214                      11                        96.92197
## 215                      11                        96.92197
## 216                      11                        96.92197
## 217                       9                       229.78020
## 218                       9                       229.78020
## 219                       9                       229.78020
## 220                       9                       229.78020
## 221                       9                       229.78020
## 222                       9                       229.78020
## 223                       9                       229.78020
## 224                       9                       229.78020
## 225                       9                       229.78020
## 226                       9                       229.78020
## 227                       9                       229.78020
## 228                       9                       229.78020
## 229                       9                       229.78020
## 230                       9                       229.78020
## 231                       9                       229.78020
## 232                       9                       229.78020
## 233                       9                       229.78020
## 234                       9                       229.78020
## 235                       9                       229.78020
## 236                       9                       229.78020
## 237                       9                       229.78020
## 238                       9                       229.78020
## 239                       9                       229.78020
## 240                       9                       229.78020
## 241                       8                       133.25628
## 242                       8                       133.25628
## 243                       8                       133.25628
## 244                       8                       133.25628
## 245                       8                       133.25628
## 246                       8                       133.25628
## 247                       8                       133.25628
## 248                       8                       133.25628
## 249                       8                       133.25628
## 250                       8                       133.25628
## 251                       8                       133.25628
## 252                       8                       133.25628
## 253                       8                       133.25628
## 254                       8                       133.25628
## 255                       8                       133.25628
## 256                       8                       133.25628
## 257                       8                       133.25628
## 258                       8                       133.25628
## 259                       8                       133.25628
## 260                       8                       133.25628
## 261                       8                       133.25628
## 262                       8                       133.25628
## 263                       8                       133.25628
## 264                       8                       133.25628
## 265                       9                       209.35334
## 266                       9                       209.35334
## 267                       9                       209.35334
## 268                       9                       209.35334
## 269                       9                       209.35334
## 270                       9                       209.35334
## 271                       9                       209.35334
## 272                       9                       209.35334
## 273                       9                       209.35334
## 274                       9                       209.35334
## 275                       9                       209.35334
## 276                       9                       209.35334
## 277                       9                       209.35334
## 278                       9                       209.35334
## 279                       9                       209.35334
## 280                       9                       209.35334
## 281                       9                       209.35334
## 282                       9                       209.35334
## 283                       9                       209.35334
## 284                       9                       209.35334
## 285                       9                       209.35334
## 286                       9                       209.35334
## 287                       9                       209.35334
## 288                       9                       209.35334
## 289                       8                       176.95269
## 290                       8                       176.95269
## 291                       8                       176.95269
## 292                       8                       176.95269
## 293                       8                       176.95269
## 294                       8                       176.95269
## 295                       8                       176.95269
## 296                       8                       176.95269
## 297                       8                       176.95269
## 298                       8                       176.95269
## 299                       8                       176.95269
## 300                       8                       176.95269
## 301                       8                       176.95269
## 302                       8                       176.95269
## 303                       8                       176.95269
## 304                       8                       176.95269
## 305                       8                       176.95269
## 306                       8                       176.95269
## 307                       8                       176.95269
## 308                       8                       176.95269
## 309                       8                       176.95269
## 310                       8                       176.95269
## 311                       8                       176.95269
## 312                       8                       176.95269
## 313                       8                       119.42234
## 314                       8                       119.42234
## 315                       8                       119.42234
## 316                       8                       119.42234
## 317                       8                       119.42234
## 318                       8                       119.42234
## 319                       8                       119.42234
## 320                       8                       119.42234
## 321                       8                       119.42234
## 322                       8                       119.42234
## 323                       8                       119.42234
## 324                       8                       119.42234
## 325                       8                       119.42234
## 326                       8                       119.42234
## 327                       8                       119.42234
## 328                       8                       119.42234
## 329                       8                       119.42234
## 330                       8                       119.42234
## 331                       8                       119.42234
## 332                       8                       119.42234
## 333                       8                       119.42234
## 334                       8                       119.42234
## 335                       8                       119.42234
## 336                       8                       119.42234
## 337                       8                       105.58980
## 338                       8                       105.58980
## 339                       8                       105.58980
## 340                       8                       105.58980
## 341                       8                       105.58980
## 342                       8                       105.58980
## 343                       8                       105.58980
## 344                       8                       105.58980
## 345                       8                       105.58980
## 346                       8                       105.58980
## 347                       8                       105.58980
## 348                       8                       105.58980
## 349                       8                       105.58980
## 350                       8                       105.58980
## 351                       8                       105.58980
## 352                       8                       105.58980
## 353                       8                       105.58980
## 354                       8                       105.58980
## 355                       8                       105.58980
## 356                       8                       105.58980
## 357                       8                       105.58980
## 358                       8                       105.58980
## 359                       8                       105.58980
## 360                       8                       105.58980
## 361                       8                        70.36451
## 362                       8                        70.36451
## 363                       8                        70.36451
## 364                       8                        70.36451
## 365                       8                        70.36451
## 366                       8                        70.36451
## 367                       8                        70.36451
## 368                       8                        70.36451
## 369                       8                        70.36451
## 370                       8                        70.36451
## 371                       8                        70.36451
## 372                       8                        70.36451
## 373                       8                        70.36451
## 374                       8                        70.36451
## 375                       8                        70.36451
## 376                       8                        70.36451
## 377                       8                        70.36451
## 378                       8                        70.36451
## 379                       8                        70.36451
## 380                       8                        70.36451
## 381                       8                        70.36451
## 382                       8                        70.36451
## 383                       8                        70.36451
## 384                       8                        70.36451
## 385                      11                        96.92197
## 386                      11                        96.92197
## 387                      11                        96.92197
## 388                      11                        96.92197
## 389                      11                        96.92197
## 390                      11                        96.92197
## 391                      11                        96.92197
## 392                      11                        96.92197
## 393                      11                        96.92197
## 394                      11                        96.92197
## 395                      11                        96.92197
## 396                      11                        96.92197
## 397                      11                        96.92197
## 398                      11                        96.92197
## 399                      11                        96.92197
## 400                      11                        96.92197
## 401                      11                        96.92197
## 402                      11                        96.92197
## 403                      11                        96.92197
## 404                      11                        96.92197
## 405                      11                        96.92197
## 406                      11                        96.92197
## 407                      11                        96.92197
## 408                      11                        96.92197
## 409                      10                       184.49614
## 410                      10                       184.49614
## 411                      10                       184.49614
## 412                      10                       184.49614
## 413                      10                       184.49614
## 414                      10                       184.49614
## 415                      10                       184.49614
## 416                      10                       184.49614
## 417                      10                       184.49614
## 418                      10                       184.49614
## 419                      10                       184.49614
## 420                      10                       184.49614
## 421                      10                       184.49614
## 422                      10                       184.49614
## 423                      10                       184.49614
## 424                      10                       184.49614
## 425                      10                       184.49614
## 426                      10                       184.49614
## 427                      10                       184.49614
## 428                      10                       184.49614
## 429                      10                       184.49614
## 430                      10                       184.49614
## 431                      10                       184.49614
## 432                      10                       184.49614
## 433                      10                       183.48227
## 434                      10                       183.48227
## 435                      10                       183.48227
## 436                      10                       183.48227
## 437                      10                       183.48227
## 438                      10                       183.48227
## 439                      10                       183.48227
## 440                      10                       183.48227
## 441                      10                       183.48227
## 442                      10                       183.48227
## 443                      10                       183.48227
## 444                      10                       183.48227
## 445                      10                       183.48227
## 446                      10                       183.48227
## 447                      10                       183.48227
## 448                      10                       183.48227
## 449                      10                       183.48227
## 450                      10                       183.48227
## 451                      10                       183.48227
## 452                      10                       183.48227
## 453                      10                       183.48227
## 454                      10                       183.48227
## 455                      10                       183.48227
## 456                      10                       183.48227
## 457                       9                       141.08208
## 458                       9                       141.08208
## 459                       9                       141.08208
## 460                       9                       141.08208
## 461                       9                       141.08208
## 462                       9                       141.08208
## 463                       9                       141.08208
## 464                       9                       141.08208
## 465                       9                       141.08208
## 466                       9                       141.08208
## 467                       9                       141.08208
## 468                       9                       141.08208
## 469                       9                       141.08208
## 470                       9                       141.08208
## 471                       9                       141.08208
## 472                       9                       141.08208
## 473                       9                       141.08208
## 474                       9                       141.08208
## 475                       9                       141.08208
## 476                       9                       141.08208
## 477                       9                       141.08208
## 478                       9                       141.08208
## 479                       9                       141.08208
## 480                       9                       141.08208
## 481                       9                       156.15050
## 482                       9                       156.15050
## 483                       9                       156.15050
## 484                       9                       156.15050
## 485                       9                       156.15050
## 486                       9                       156.15050
## 487                       9                       156.15050
## 488                       9                       156.15050
## 489                       9                       156.15050
## 490                       9                       156.15050
## 491                       9                       156.15050
## 492                       9                       156.15050
## 493                       9                       156.15050
## 494                       9                       156.15050
## 495                       9                       156.15050
## 496                       9                       156.15050
## 497                       9                       156.15050
## 498                       9                       156.15050
## 499                       9                       156.15050
## 500                       9                       156.15050
## 501                       9                       156.15050
## 502                       9                       156.15050
## 503                       9                       156.15050
## 504                       9                       156.15050
## 505                       6                       140.12740
## 506                       6                       140.12740
## 507                       6                       140.12740
## 508                       6                       140.12740
## 509                       6                       140.12740
## 510                       6                       140.12740
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## 2012                      8                       196.58628
## 2013                      8                       196.58628
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## 2575                      7                       112.16981
## 2576                      7                       112.16981
## 2577                      7                       112.16981
## 2578                      7                       112.16981
## 2579                      7                       112.16981
## 2580                      7                       112.16981
## 2581                      7                       112.16981
## 2582                      7                       112.16981
## 2583                      7                       112.16981
## 2584                      7                       112.16981
## 2585                      7                       112.16981
## 2586                      7                       112.16981
## 2587                      7                       112.16981
## 2588                      7                       112.16981
## 2589                      7                       112.16981
## 2590                      7                       112.16981
## 2591                      7                       112.16981
## 2592                      7                       112.16981
## 2593                      7                       151.62447
## 2594                      7                       151.62447
## 2595                      7                       151.62447
## 2596                      7                       151.62447
## 2597                      7                       151.62447
## 2598                      7                       151.62447
## 2599                      7                       151.62447
## 2600                      7                       151.62447
## 2601                      7                       151.62447
## 2602                      7                       151.62447
## 2603                      7                       151.62447
## 2604                      7                       151.62447
## 2605                      7                       151.62447
## 2606                      7                       151.62447
## 2607                      7                       151.62447
## 2608                      7                       151.62447
## 2609                      7                       151.62447
## 2610                      7                       151.62447
## 2611                      7                       151.62447
## 2612                      7                       151.62447
## 2613                      7                       151.62447
## 2614                      7                       151.62447
## 2615                      7                       151.62447
## 2616                      7                       151.62447
## 2617                      6                        59.47007
## 2618                      6                        59.47007
## 2619                      6                        59.47007
## 2620                      6                        59.47007
## 2621                      6                        59.47007
## 2622                      6                        59.47007
## 2623                      6                        59.47007
## 2624                      6                        59.47007
## 2625                      6                        59.47007
## 2626                      6                        59.47007
## 2627                      6                        59.47007
## 2628                      6                        59.47007
## 2629                      6                        59.47007
## 2630                      6                        59.47007
## 2631                      6                        59.47007
## 2632                      6                        59.47007
## 2633                      6                        59.47007
## 2634                      6                        59.47007
## 2635                      6                        59.47007
## 2636                      6                        59.47007
## 2637                      6                        59.47007
## 2638                      6                        59.47007
## 2639                      6                        59.47007
## 2640                      6                        59.47007
## 2641                      7                        39.56420
## 2642                      7                        39.56420
## 2643                      7                        39.56420
## 2644                      7                        39.56420
## 2645                      7                        39.56420
## 2646                      7                        39.56420
## 2647                      7                        39.56420
## 2648                      7                        39.56420
## 2649                      7                        39.56420
## 2650                      7                        39.56420
## 2651                      7                        39.56420
## 2652                      7                        39.56420
## 2653                      7                        39.56420
## 2654                      7                        39.56420
## 2655                      7                        39.56420
## 2656                      7                        39.56420
## 2657                      7                        39.56420
## 2658                      7                        39.56420
## 2659                      7                        39.56420
## 2660                      7                        39.56420
## 2661                      7                        39.56420
## 2662                      7                        39.56420
## 2663                      7                        39.56420
## 2664                      7                        39.56420
## 2665                      6                        33.29667
## 2666                      6                        33.29667
## 2667                      6                        33.29667
## 2668                      6                        33.29667
## 2669                      6                        33.29667
## 2670                      6                        33.29667
## 2671                      6                        33.29667
## 2672                      6                        33.29667
## 2673                      6                        33.29667
## 2674                      6                        33.29667
## 2675                      6                        33.29667
## 2676                      6                        33.29667
## 2677                      6                        33.29667
## 2678                      6                        33.29667
## 2679                      6                        33.29667
## 2680                      6                        33.29667
## 2681                      6                        33.29667
## 2682                      6                        33.29667
## 2683                      6                        33.29667
## 2684                      6                        33.29667
## 2685                      6                        33.29667
## 2686                      6                        33.29667
## 2687                      6                        33.29667
## 2688                      6                        33.29667
## 2689                     11                        96.92197
## 2690                     11                        96.92197
## 2691                     11                        96.92197
## 2692                     11                        96.92197
## 2693                     11                        96.92197
## 2694                     11                        96.92197
## 2695                     11                        96.92197
## 2696                     11                        96.92197
## 2697                     11                        96.92197
## 2698                     11                        96.92197
## 2699                     11                        96.92197
## 2700                     11                        96.92197
## 2701                     11                        96.92197
## 2702                     11                        96.92197
## 2703                     11                        96.92197
## 2704                     11                        96.92197
## 2705                     11                        96.92197
## 2706                     11                        96.92197
## 2707                     11                        96.92197
## 2708                     11                        96.92197
## 2709                     11                        96.92197
## 2710                     11                        96.92197
## 2711                     11                        96.92197
## 2712                     11                        96.92197
## 2713                      9                       119.13585
## 2714                      9                       119.13585
## 2715                      9                       119.13585
## 2716                      9                       119.13585
## 2717                      9                       119.13585
## 2718                      9                       119.13585
## 2719                      9                       119.13585
## 2720                      9                       119.13585
## 2721                      9                       119.13585
## 2722                      9                       119.13585
## 2723                      9                       119.13585
## 2724                      9                       119.13585
## 2725                      9                       119.13585
## 2726                      9                       119.13585
## 2727                      9                       119.13585
## 2728                      9                       119.13585
## 2729                      9                       119.13585
## 2730                      9                       119.13585
## 2731                      9                       119.13585
## 2732                      9                       119.13585
## 2733                      9                       119.13585
## 2734                      9                       119.13585
## 2735                      9                       119.13585
## 2736                      9                       119.13585
## 2737                      7                       149.70690
## 2738                      7                       149.70690
## 2739                      7                       149.70690
## 2740                      7                       149.70690
## 2741                      7                       149.70690
## 2742                      7                       149.70690
## 2743                      7                       149.70690
## 2744                      7                       149.70690
## 2745                      7                       149.70690
## 2746                      7                       149.70690
## 2747                      7                       149.70690
## 2748                      7                       149.70690
## 2749                      7                       149.70690
## 2750                      7                       149.70690
## 2751                      7                       149.70690
## 2752                      7                       149.70690
## 2753                      7                       149.70690
## 2754                      7                       149.70690
## 2755                      7                       149.70690
## 2756                      7                       149.70690
## 2757                      7                       149.70690
## 2758                      7                       149.70690
## 2759                      7                       149.70690
## 2760                      7                       149.70690
## 2761                      8                       205.19359
## 2762                      8                       205.19359
## 2763                      8                       205.19359
## 2764                      8                       205.19359
## 2765                      8                       205.19359
## 2766                      8                       205.19359
## 2767                      8                       205.19359
## 2768                      8                       205.19359
## 2769                      8                       205.19359
## 2770                      8                       205.19359
## 2771                      8                       205.19359
## 2772                      8                       205.19359
## 2773                      8                       205.19359
## 2774                      8                       205.19359
## 2775                      8                       205.19359
## 2776                      8                       205.19359
## 2777                      8                       205.19359
## 2778                      8                       205.19359
## 2779                      8                       205.19359
## 2780                      8                       205.19359
## 2781                      8                       205.19359
## 2782                      8                       205.19359
## 2783                      8                       205.19359
## 2784                      8                       205.19359
## 2785                      9                       210.11345
## 2786                      9                       210.11345
## 2787                      9                       210.11345
## 2788                      9                       210.11345
## 2789                      9                       210.11345
## 2790                      9                       210.11345
## 2791                      9                       210.11345
## 2792                      9                       210.11345
## 2793                      9                       210.11345
## 2794                      9                       210.11345
## 2795                      9                       210.11345
## 2796                      9                       210.11345
## 2797                      9                       210.11345
## 2798                      9                       210.11345
## 2799                      9                       210.11345
## 2800                      9                       210.11345
## 2801                      9                       210.11345
## 2802                      9                       210.11345
## 2803                      9                       210.11345
## 2804                      9                       210.11345
## 2805                      9                       210.11345
## 2806                      9                       210.11345
## 2807                      9                       210.11345
## 2808                      9                       210.11345
## 2809                      9                       170.39894
## 2810                      9                       170.39894
## 2811                      9                       170.39894
## 2812                      9                       170.39894
## 2813                      9                       170.39894
## 2814                      9                       170.39894
## 2815                      9                       170.39894
## 2816                      9                       170.39894
## 2817                      9                       170.39894
## 2818                      9                       170.39894
## 2819                      9                       170.39894
## 2820                      9                       170.39894
## 2821                      9                       170.39894
## 2822                      9                       170.39894
## 2823                      9                       170.39894
## 2824                      9                       170.39894
## 2825                      9                       170.39894
## 2826                      9                       170.39894
## 2827                      9                       170.39894
## 2828                      9                       170.39894
## 2829                      9                       170.39894
## 2830                      9                       170.39894
## 2831                      9                       170.39894
## 2832                      9                       170.39894
## 2833                      8                       149.41666
## 2834                      8                       149.41666
## 2835                      8                       149.41666
## 2836                      8                       149.41666
## 2837                      8                       149.41666
## 2838                      8                       149.41666
## 2839                      8                       149.41666
## 2840                      8                       149.41666
## 2841                      8                       149.41666
## 2842                      8                       149.41666
## 2843                      8                       149.41666
## 2844                      8                       149.41666
## 2845                      8                       149.41666
## 2846                      8                       149.41666
## 2847                      8                       149.41666
## 2848                      8                       149.41666
## 2849                      8                       149.41666
## 2850                      8                       149.41666
## 2851                      8                       149.41666
## 2852                      8                       149.41666
## 2853                      8                       149.41666
## 2854                      8                       149.41666
## 2855                      8                       149.41666
## 2856                      8                       149.41666
## 2857                      9                       111.86388
## 2858                      9                       111.86388
## 2859                      9                       111.86388
## 2860                      9                       111.86388
## 2861                      9                       111.86388
## 2862                      9                       111.86388
## 2863                      9                       111.86388
## 2864                      9                       111.86388
## 2865                      9                       111.86388
## 2866                      9                       111.86388
## 2867                      9                       111.86388
## 2868                      9                       111.86388
## 2869                      9                       111.86388
## 2870                      9                       111.86388
## 2871                      9                       111.86388
## 2872                      9                       111.86388
## 2873                      9                       111.86388
## 2874                      9                       111.86388
## 2875                      9                       111.86388
## 2876                      9                       111.86388
## 2877                      9                       111.86388
## 2878                      9                       111.86388
## 2879                      9                       111.86388
## 2880                      9                       111.86388
## 2881                     11                        96.92197
## 2882                     11                        96.92197
## 2883                     11                        96.92197
## 2884                     11                        96.92197
## 2885                     11                        96.92197
## 2886                     11                        96.92197
## 2887                     11                        96.92197
## 2888                     11                        96.92197
## 2889                     11                        96.92197
## 2890                     11                        96.92197
## 2891                     11                        96.92197
## 2892                     11                        96.92197
## 2893                     11                        96.92197
## 2894                     11                        96.92197
## 2895                     11                        96.92197
## 2896                     11                        96.92197
## 2897                     11                        96.92197
## 2898                     11                        96.92197
## 2899                     11                        96.92197
## 2900                     11                        96.92197
## 2901                     11                        96.92197
## 2902                     11                        96.92197
## 2903                     11                        96.92197
## 2904                     11                        96.92197
## 2905                      9                       149.85701
## 2906                      9                       149.85701
## 2907                      9                       149.85701
## 2908                      9                       149.85701
## 2909                      9                       149.85701
## 2910                      9                       149.85701
## 2911                      9                       149.85701
## 2912                      9                       149.85701
## 2913                      9                       149.85701
## 2914                      9                       149.85701
## 2915                      9                       149.85701
## 2916                      9                       149.85701
## 2917                      9                       149.85701
## 2918                      9                       149.85701
## 2919                      9                       149.85701
## 2920                      9                       149.85701
## 2921                      9                       149.85701
## 2922                      9                       149.85701
## 2923                      9                       149.85701
## 2924                      9                       149.85701
## 2925                      9                       149.85701
## 2926                      9                       149.85701
## 2927                      9                       149.85701
## 2928                      9                       149.85701
## 2929                     10                       158.73461
## 2930                     10                       158.73461
## 2931                     10                       158.73461
## 2932                     10                       158.73461
## 2933                     10                       158.73461
## 2934                     10                       158.73461
## 2935                     10                       158.73461
## 2936                     10                       158.73461
## 2937                     10                       158.73461
## 2938                     10                       158.73461
## 2939                     10                       158.73461
## 2940                     10                       158.73461
## 2941                     10                       158.73461
## 2942                     10                       158.73461
## 2943                     10                       158.73461
## 2944                     10                       158.73461
## 2945                     10                       158.73461
## 2946                     10                       158.73461
## 2947                     10                       158.73461
## 2948                     10                       158.73461
## 2949                     10                       158.73461
## 2950                     10                       158.73461
## 2951                     10                       158.73461
## 2952                     10                       158.73461
## 2953                      8                       185.82102
## 2954                      8                       185.82102
## 2955                      8                       185.82102
## 2956                      8                       185.82102
## 2957                      8                       185.82102
## 2958                      8                       185.82102
## 2959                      8                       185.82102
## 2960                      8                       185.82102
## 2961                      8                       185.82102
## 2962                      8                       185.82102
## 2963                      8                       185.82102
## 2964                      8                       185.82102
## 2965                      8                       185.82102
## 2966                      8                       185.82102
## 2967                      8                       185.82102
## 2968                      8                       185.82102
## 2969                      8                       185.82102
## 2970                      8                       185.82102
## 2971                      8                       185.82102
## 2972                      8                       185.82102
## 2973                      8                       185.82102
## 2974                      8                       185.82102
## 2975                      8                       185.82102
## 2976                      8                       185.82102
## 2977                      8                       134.71835
## 2978                      8                       134.71835
## 2979                      8                       134.71835
## 2980                      8                       134.71835
## 2981                      8                       134.71835
## 2982                      8                       134.71835
## 2983                      8                       134.71835
## 2984                      8                       134.71835
## 2985                      8                       134.71835
## 2986                      8                       134.71835
## 2987                      8                       134.71835
## 2988                      8                       134.71835
## 2989                      8                       134.71835
## 2990                      8                       134.71835
## 2991                      8                       134.71835
## 2992                      8                       134.71835
## 2993                      8                       134.71835
## 2994                      8                       134.71835
## 2995                      8                       134.71835
## 2996                      8                       134.71835
## 2997                      8                       134.71835
## 2998                      8                       134.71835
## 2999                      8                       134.71835
## 3000                      8                       134.71835
## 3001                      6                       117.16941
## 3002                      6                       117.16941
## 3003                      6                       117.16941
## 3004                      6                       117.16941
## 3005                      6                       117.16941
## 3006                      6                       117.16941
## 3007                      6                       117.16941
## 3008                      6                       117.16941
## 3009                      6                       117.16941
## 3010                      6                       117.16941
## 3011                      6                       117.16941
## 3012                      6                       117.16941
## 3013                      6                       117.16941
## 3014                      6                       117.16941
## 3015                      6                       117.16941
## 3016                      6                       117.16941
## 3017                      6                       117.16941
## 3018                      6                       117.16941
## 3019                      6                       117.16941
## 3020                      6                       117.16941
## 3021                      6                       117.16941
## 3022                      6                       117.16941
## 3023                      6                       117.16941
## 3024                      6                       117.16941
## 3025                      8                       102.14115
## 3026                      8                       102.14115
## 3027                      8                       102.14115
## 3028                      8                       102.14115
## 3029                      8                       102.14115
## 3030                      8                       102.14115
## 3031                      8                       102.14115
## 3032                      8                       102.14115
## 3033                      8                       102.14115
## 3034                      8                       102.14115
## 3035                      8                       102.14115
## 3036                      8                       102.14115
## 3037                      8                       102.14115
## 3038                      8                       102.14115
## 3039                      8                       102.14115
## 3040                      8                       102.14115
## 3041                      8                       102.14115
## 3042                      8                       102.14115
## 3043                      8                       102.14115
## 3044                      8                       102.14115
## 3045                      8                       102.14115
## 3046                      8                       102.14115
## 3047                      8                       102.14115
## 3048                      8                       102.14115
## 3049                      9                        93.17670
## 3050                      9                        93.17670
## 3051                      9                        93.17670
## 3052                      9                        93.17670
## 3053                      9                        93.17670
## 3054                      9                        93.17670
## 3055                      9                        93.17670
## 3056                      9                        93.17670
## 3057                      9                        93.17670
## 3058                      9                        93.17670
## 3059                      9                        93.17670
## 3060                      9                        93.17670
## 3061                      9                        93.17670
## 3062                      9                        93.17670
## 3063                      9                        93.17670
## 3064                      9                        93.17670
## 3065                      9                        93.17670
## 3066                      9                        93.17670
## 3067                      9                        93.17670
## 3068                      9                        93.17670
## 3069                      9                        93.17670
## 3070                      9                        93.17670
## 3071                      9                        93.17670
## 3072                      9                        93.17670
## 3073                     11                        96.92197
## 3074                     11                        96.92197
## 3075                     11                        96.92197
## 3076                     11                        96.92197
## 3077                     11                        96.92197
## 3078                     11                        96.92197
## 3079                     11                        96.92197
## 3080                     11                        96.92197
## 3081                     11                        96.92197
## 3082                     11                        96.92197
## 3083                     11                        96.92197
## 3084                     11                        96.92197
## 3085                     11                        96.92197
## 3086                     11                        96.92197
## 3087                     11                        96.92197
## 3088                     11                        96.92197
## 3089                     11                        96.92197
## 3090                     11                        96.92197
## 3091                     11                        96.92197
## 3092                     11                        96.92197
## 3093                     11                        96.92197
## 3094                     11                        96.92197
## 3095                     11                        96.92197
## 3096                     11                        96.92197
## 3097                     10                       226.72885
## 3098                     10                       226.72885
## 3099                     10                       226.72885
## 3100                     10                       226.72885
## 3101                     10                       226.72885
## 3102                     10                       226.72885
## 3103                     10                       226.72885
## 3104                     10                       226.72885
## 3105                     10                       226.72885
## 3106                     10                       226.72885
## 3107                     10                       226.72885
## 3108                     10                       226.72885
## 3109                     10                       226.72885
## 3110                     10                       226.72885
## 3111                     10                       226.72885
## 3112                     10                       226.72885
## 3113                     10                       226.72885
## 3114                     10                       226.72885
## 3115                     10                       226.72885
## 3116                     10                       226.72885
## 3117                     10                       226.72885
## 3118                     10                       226.72885
## 3119                     10                       226.72885
## 3120                     10                       226.72885
## 3121                      8                       128.89784
## 3122                      8                       128.89784
## 3123                      8                       128.89784
## 3124                      8                       128.89784
## 3125                      8                       128.89784
## 3126                      8                       128.89784
## 3127                      8                       128.89784
## 3128                      8                       128.89784
## 3129                      8                       128.89784
## 3130                      8                       128.89784
## 3131                      8                       128.89784
## 3132                      8                       128.89784
## 3133                      8                       128.89784
## 3134                      8                       128.89784
## 3135                      8                       128.89784
## 3136                      8                       128.89784
## 3137                      8                       128.89784
## 3138                      8                       128.89784
## 3139                      8                       128.89784
## 3140                      8                       128.89784
## 3141                      8                       128.89784
## 3142                      8                       128.89784
## 3143                      8                       128.89784
## 3144                      8                       128.89784
## 3145                      8                       213.14406
## 3146                      8                       213.14406
## 3147                      8                       213.14406
## 3148                      8                       213.14406
## 3149                      8                       213.14406
## 3150                      8                       213.14406
## 3151                      8                       213.14406
## 3152                      8                       213.14406
## 3153                      8                       213.14406
## 3154                      8                       213.14406
## 3155                      8                       213.14406
## 3156                      8                       213.14406
## 3157                      8                       213.14406
## 3158                      8                       213.14406
## 3159                      8                       213.14406
## 3160                      8                       213.14406
## 3161                      8                       213.14406
## 3162                      8                       213.14406
## 3163                      8                       213.14406
## 3164                      8                       213.14406
## 3165                      8                       213.14406
## 3166                      8                       213.14406
## 3167                      8                       213.14406
## 3168                      8                       213.14406
## 3169                      6                       171.38523
## 3170                      6                       171.38523
## 3171                      6                       171.38523
## 3172                      6                       171.38523
## 3173                      6                       171.38523
## 3174                      6                       171.38523
## 3175                      6                       171.38523
## 3176                      6                       171.38523
## 3177                      6                       171.38523
## 3178                      6                       171.38523
## 3179                      6                       171.38523
## 3180                      6                       171.38523
## 3181                      6                       171.38523
## 3182                      6                       171.38523
## 3183                      6                       171.38523
## 3184                      6                       171.38523
## 3185                      6                       171.38523
## 3186                      6                       171.38523
## 3187                      6                       171.38523
## 3188                      6                       171.38523
## 3189                      6                       171.38523
## 3190                      6                       171.38523
## 3191                      6                       171.38523
## 3192                      6                       171.38523
## 3193                      8                       119.30850
## 3194                      8                       119.30850
## 3195                      8                       119.30850
## 3196                      8                       119.30850
## 3197                      8                       119.30850
## 3198                      8                       119.30850
## 3199                      8                       119.30850
## 3200                      8                       119.30850
## 3201                      8                       119.30850
## 3202                      8                       119.30850
## 3203                      8                       119.30850
## 3204                      8                       119.30850
## 3205                      8                       119.30850
## 3206                      8                       119.30850
## 3207                      8                       119.30850
## 3208                      8                       119.30850
## 3209                      8                       119.30850
## 3210                      8                       119.30850
## 3211                      8                       119.30850
## 3212                      8                       119.30850
## 3213                      8                       119.30850
## 3214                      8                       119.30850
## 3215                      8                       119.30850
## 3216                      8                       119.30850
## 3217                      7                       103.92120
## 3218                      7                       103.92120
## 3219                      7                       103.92120
## 3220                      7                       103.92120
## 3221                      7                       103.92120
## 3222                      7                       103.92120
## 3223                      7                       103.92120
## 3224                      7                       103.92120
## 3225                      7                       103.92120
##      total_metaecosystem_Ble_indiv total_metaecosystem_Cep_indiv
## 1                         217.1512                      1794.767
## 2                         217.1512                      1794.767
## 3                         217.1512                      1794.767
## 4                         217.1512                      1794.767
## 5                         217.1512                      1794.767
## 6                         217.1512                      1794.767
## 7                         217.1512                      1794.767
## 8                         217.1512                      1794.767
## 9                         217.1512                      1794.767
## 10                        217.1512                      1794.767
## 11                        217.1512                      1794.767
## 12                        217.1512                      1794.767
## 13                        217.1512                      1794.767
## 14                        217.1512                      1794.767
## 15                        217.1512                      1794.767
## 16                        217.1512                      1794.767
## 17                        217.1512                      1794.767
## 18                        217.1512                      1794.767
## 19                        217.1512                      1794.767
## 20                        217.1512                      1794.767
## 21                        217.1512                      1794.767
## 22                        217.1512                      1794.767
## 23                        217.1512                      1794.767
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## 1537                      217.1512                      1794.767
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## 1596                     1796.5116                     20522.093
## 1597                     1796.5116                     20522.093
## 1598                     1796.5116                     20522.093
## 1599                     1796.5116                     20522.093
## 1600                     1796.5116                     20522.093
## 1601                     1796.5116                     20522.093
## 1602                     1796.5116                     20522.093
## 1603                     1796.5116                     20522.093
## 1604                     1796.5116                     20522.093
## 1605                     1796.5116                     20522.093
## 1606                     1796.5116                     20522.093
## 1607                     1796.5116                     20522.093
## 1608                     1796.5116                     20522.093
## 1609                     2616.2791                     11761.047
## 1610                     2616.2791                     11761.047
## 1611                     2616.2791                     11761.047
## 1612                     2616.2791                     11761.047
## 1613                     2616.2791                     11761.047
## 1614                     2616.2791                     11761.047
## 1615                     2616.2791                     11761.047
## 1616                     2616.2791                     11761.047
## 1617                     2616.2791                     11761.047
## 1618                     2616.2791                     11761.047
## 1619                     2616.2791                     11761.047
## 1620                     2616.2791                     11761.047
## 1621                     2616.2791                     11761.047
## 1622                     2616.2791                     11761.047
## 1623                     2616.2791                     11761.047
## 1624                     2616.2791                     11761.047
## 1625                     2616.2791                     11761.047
## 1626                     2616.2791                     11761.047
## 1627                     2616.2791                     11761.047
## 1628                     2616.2791                     11761.047
## 1629                     2616.2791                     11761.047
## 1630                     2616.2791                     11761.047
## 1631                     2616.2791                     11761.047
## 1632                     2616.2791                     11761.047
## 1633                     3680.2326                     10379.651
## 1634                     3680.2326                     10379.651
## 1635                     3680.2326                     10379.651
## 1636                     3680.2326                     10379.651
## 1637                     3680.2326                     10379.651
## 1638                     3680.2326                     10379.651
## 1639                     3680.2326                     10379.651
## 1640                     3680.2326                     10379.651
## 1641                     3680.2326                     10379.651
## 1642                     3680.2326                     10379.651
## 1643                     3680.2326                     10379.651
## 1644                     3680.2326                     10379.651
## 1645                     3680.2326                     10379.651
## 1646                     3680.2326                     10379.651
## 1647                     3680.2326                     10379.651
## 1648                     3680.2326                     10379.651
## 1649                     3680.2326                     10379.651
## 1650                     3680.2326                     10379.651
## 1651                     3680.2326                     10379.651
## 1652                     3680.2326                     10379.651
## 1653                     3680.2326                     10379.651
## 1654                     3680.2326                     10379.651
## 1655                     3680.2326                     10379.651
## 1656                     3680.2326                     10379.651
## 1657                     4360.4651                      4901.163
## 1658                     4360.4651                      4901.163
## 1659                     4360.4651                      4901.163
## 1660                     4360.4651                      4901.163
## 1661                     4360.4651                      4901.163
## 1662                     4360.4651                      4901.163
## 1663                     4360.4651                      4901.163
## 1664                     4360.4651                      4901.163
## 1665                     4360.4651                      4901.163
## 1666                     4360.4651                      4901.163
## 1667                     4360.4651                      4901.163
## 1668                     4360.4651                      4901.163
## 1669                     4360.4651                      4901.163
## 1670                     4360.4651                      4901.163
## 1671                     4360.4651                      4901.163
## 1672                     4360.4651                      4901.163
## 1673                     4360.4651                      4901.163
## 1674                     4360.4651                      4901.163
## 1675                     4360.4651                      4901.163
## 1676                     4360.4651                      4901.163
## 1677                     4360.4651                      4901.163
## 1678                     4360.4651                      4901.163
## 1679                     4360.4651                      4901.163
## 1680                     4360.4651                      4901.163
## 1681                     1090.1163                      4332.558
## 1682                     1090.1163                      4332.558
## 1683                     1090.1163                      4332.558
## 1684                     1090.1163                      4332.558
## 1685                     1090.1163                      4332.558
## 1686                     1090.1163                      4332.558
## 1687                     1090.1163                      4332.558
## 1688                     1090.1163                      4332.558
## 1689                     1090.1163                      4332.558
## 1690                     1090.1163                      4332.558
## 1691                     1090.1163                      4332.558
## 1692                     1090.1163                      4332.558
## 1693                     1090.1163                      4332.558
## 1694                     1090.1163                      4332.558
## 1695                     1090.1163                      4332.558
## 1696                     1090.1163                      4332.558
## 1697                     1090.1163                      4332.558
## 1698                     1090.1163                      4332.558
## 1699                     1090.1163                      4332.558
## 1700                     1090.1163                      4332.558
## 1701                     1090.1163                      4332.558
## 1702                     1090.1163                      4332.558
## 1703                     1090.1163                      4332.558
## 1704                     1090.1163                      4332.558
## 1705                     2180.2326                      2048.547
## 1706                     2180.2326                      2048.547
## 1707                     2180.2326                      2048.547
## 1708                     2180.2326                      2048.547
## 1709                     2180.2326                      2048.547
## 1710                     2180.2326                      2048.547
## 1711                     2180.2326                      2048.547
## 1712                     2180.2326                      2048.547
## 1713                     2180.2326                      2048.547
## 1714                     2180.2326                      2048.547
## 1715                     2180.2326                      2048.547
## 1716                     2180.2326                      2048.547
## 1717                     2180.2326                      2048.547
## 1718                     2180.2326                      2048.547
## 1719                     2180.2326                      2048.547
## 1720                     2180.2326                      2048.547
## 1721                     2180.2326                      2048.547
## 1722                     2180.2326                      2048.547
## 1723                     2180.2326                      2048.547
## 1724                     2180.2326                      2048.547
## 1725                     2180.2326                      2048.547
## 1726                     2180.2326                      2048.547
## 1727                     2180.2326                      2048.547
## 1728                     2180.2326                      2048.547
## 1729                      217.1512                      1794.767
## 1730                      217.1512                      1794.767
## 1731                      217.1512                      1794.767
## 1732                      217.1512                      1794.767
## 1733                      217.1512                      1794.767
## 1734                      217.1512                      1794.767
## 1735                      217.1512                      1794.767
## 1736                      217.1512                      1794.767
## 1737                      217.1512                      1794.767
## 1738                      217.1512                      1794.767
## 1739                      217.1512                      1794.767
## 1740                      217.1512                      1794.767
## 1741                      217.1512                      1794.767
## 1742                      217.1512                      1794.767
## 1743                      217.1512                      1794.767
## 1744                      217.1512                      1794.767
## 1745                      217.1512                      1794.767
## 1746                      217.1512                      1794.767
## 1747                      217.1512                      1794.767
## 1748                      217.1512                      1794.767
## 1749                      217.1512                      1794.767
## 1750                      217.1512                      1794.767
## 1751                      217.1512                      1794.767
## 1752                      217.1512                      1794.767
## 1753                     1090.1163                      7660.465
## 1754                     1090.1163                      7660.465
## 1755                     1090.1163                      7660.465
## 1756                     1090.1163                      7660.465
## 1757                     1090.1163                      7660.465
## 1758                     1090.1163                      7660.465
## 1759                     1090.1163                      7660.465
## 1760                     1090.1163                      7660.465
## 1761                     1090.1163                      7660.465
## 1762                     1090.1163                      7660.465
## 1763                     1090.1163                      7660.465
## 1764                     1090.1163                      7660.465
## 1765                     1090.1163                      7660.465
## 1766                     1090.1163                      7660.465
## 1767                     1090.1163                      7660.465
## 1768                     1090.1163                      7660.465
## 1769                     1090.1163                      7660.465
## 1770                     1090.1163                      7660.465
## 1771                     1090.1163                      7660.465
## 1772                     1090.1163                      7660.465
## 1773                     1090.1163                      7660.465
## 1774                     1090.1163                      7660.465
## 1775                     1090.1163                      7660.465
## 1776                     1090.1163                      7660.465
## 1777                     2886.6279                     13658.721
## 1778                     2886.6279                     13658.721
## 1779                     2886.6279                     13658.721
## 1780                     2886.6279                     13658.721
## 1781                     2886.6279                     13658.721
## 1782                     2886.6279                     13658.721
## 1783                     2886.6279                     13658.721
## 1784                     2886.6279                     13658.721
## 1785                     2886.6279                     13658.721
## 1786                     2886.6279                     13658.721
## 1787                     2886.6279                     13658.721
## 1788                     2886.6279                     13658.721
## 1789                     2886.6279                     13658.721
## 1790                     2886.6279                     13658.721
## 1791                     2886.6279                     13658.721
## 1792                     2886.6279                     13658.721
## 1793                     2886.6279                     13658.721
## 1794                     2886.6279                     13658.721
## 1795                     2886.6279                     13658.721
## 1796                     2886.6279                     13658.721
## 1797                     2886.6279                     13658.721
## 1798                     2886.6279                     13658.721
## 1799                     2886.6279                     13658.721
## 1800                     2886.6279                     13658.721
## 1801                     2616.2791                     10217.442
## 1802                     2616.2791                     10217.442
## 1803                     2616.2791                     10217.442
## 1804                     2616.2791                     10217.442
## 1805                     2616.2791                     10217.442
## 1806                     2616.2791                     10217.442
## 1807                     2616.2791                     10217.442
## 1808                     2616.2791                     10217.442
## 1809                     2616.2791                     10217.442
## 1810                     2616.2791                     10217.442
## 1811                     2616.2791                     10217.442
## 1812                     2616.2791                     10217.442
## 1813                     2616.2791                     10217.442
## 1814                     2616.2791                     10217.442
## 1815                     2616.2791                     10217.442
## 1816                     2616.2791                     10217.442
## 1817                     2616.2791                     10217.442
## 1818                     2616.2791                     10217.442
## 1819                     2616.2791                     10217.442
## 1820                     2616.2791                     10217.442
## 1821                     2616.2791                     10217.442
## 1822                     2616.2791                     10217.442
## 1823                     2616.2791                     10217.442
## 1824                     2616.2791                     10217.442
## 1825                     1090.1163                     12760.465
## 1826                     1090.1163                     12760.465
## 1827                     1090.1163                     12760.465
## 1828                     1090.1163                     12760.465
## 1829                     1090.1163                     12760.465
## 1830                     1090.1163                     12760.465
## 1831                     1090.1163                     12760.465
## 1832                     1090.1163                     12760.465
## 1833                     1090.1163                     12760.465
## 1834                     1090.1163                     12760.465
## 1835                     1090.1163                     12760.465
## 1836                     1090.1163                     12760.465
## 1837                     1090.1163                     12760.465
## 1838                     1090.1163                     12760.465
## 1839                     1090.1163                     12760.465
## 1840                     1090.1163                     12760.465
## 1841                     1090.1163                     12760.465
## 1842                     1090.1163                     12760.465
## 1843                     1090.1163                     12760.465
## 1844                     1090.1163                     12760.465
## 1845                     1090.1163                     12760.465
## 1846                     1090.1163                     12760.465
## 1847                     1090.1163                     12760.465
## 1848                     1090.1163                     12760.465
## 1849                     2162.7907                      8005.814
## 1850                     2162.7907                      8005.814
## 1851                     2162.7907                      8005.814
## 1852                     2162.7907                      8005.814
## 1853                     2162.7907                      8005.814
## 1854                     2162.7907                      8005.814
## 1855                     2162.7907                      8005.814
## 1856                     2162.7907                      8005.814
## 1857                     2162.7907                      8005.814
## 1858                     2162.7907                      8005.814
## 1859                     2162.7907                      8005.814
## 1860                     2162.7907                      8005.814
## 1861                     2162.7907                      8005.814
## 1862                     2162.7907                      8005.814
## 1863                     2162.7907                      8005.814
## 1864                     2162.7907                      8005.814
## 1865                     2162.7907                      8005.814
## 1866                     2162.7907                      8005.814
## 1867                     2162.7907                      8005.814
## 1868                     2162.7907                      8005.814
## 1869                     2162.7907                      8005.814
## 1870                     2162.7907                      8005.814
## 1871                     2162.7907                      8005.814
## 1872                     2162.7907                      8005.814
## 1873                     4329.9419                      9743.895
## 1874                     4329.9419                      9743.895
## 1875                     4329.9419                      9743.895
## 1876                     4329.9419                      9743.895
## 1877                     4329.9419                      9743.895
## 1878                     4329.9419                      9743.895
## 1879                     4329.9419                      9743.895
## 1880                     4329.9419                      9743.895
## 1881                     4329.9419                      9743.895
## 1882                     4329.9419                      9743.895
## 1883                     4329.9419                      9743.895
## 1884                     4329.9419                      9743.895
## 1885                     4329.9419                      9743.895
## 1886                     4329.9419                      9743.895
## 1887                     4329.9419                      9743.895
## 1888                     4329.9419                      9743.895
## 1889                     4329.9419                      9743.895
## 1890                     4329.9419                      9743.895
## 1891                     4329.9419                      9743.895
## 1892                     4329.9419                      9743.895
## 1893                     4329.9419                      9743.895
## 1894                     4329.9419                      9743.895
## 1895                     4329.9419                      9743.895
## 1896                     4329.9419                      9743.895
## 1897                     3920.0581                     16006.395
## 1898                     3920.0581                     16006.395
## 1899                     3920.0581                     16006.395
## 1900                     3920.0581                     16006.395
## 1901                     3920.0581                     16006.395
## 1902                     3920.0581                     16006.395
## 1903                     3920.0581                     16006.395
## 1904                     3920.0581                     16006.395
## 1905                     3920.0581                     16006.395
## 1906                     3920.0581                     16006.395
## 1907                     3920.0581                     16006.395
## 1908                     3920.0581                     16006.395
## 1909                     3920.0581                     16006.395
## 1910                     3920.0581                     16006.395
## 1911                     3920.0581                     16006.395
## 1912                     3920.0581                     16006.395
## 1913                     3920.0581                     16006.395
## 1914                     3920.0581                     16006.395
## 1915                     3920.0581                     16006.395
## 1916                     3920.0581                     16006.395
## 1917                     3920.0581                     16006.395
## 1918                     3920.0581                     16006.395
## 1919                     3920.0581                     16006.395
## 1920                     3920.0581                     16006.395
## 1921                      217.1512                      1794.767
## 1922                      217.1512                      1794.767
## 1923                      217.1512                      1794.767
## 1924                      217.1512                      1794.767
## 1925                      217.1512                      1794.767
## 1926                      217.1512                      1794.767
## 1927                      217.1512                      1794.767
## 1928                      217.1512                      1794.767
## 1929                      217.1512                      1794.767
## 1930                      217.1512                      1794.767
## 1931                      217.1512                      1794.767
## 1932                      217.1512                      1794.767
## 1933                      217.1512                      1794.767
## 1934                      217.1512                      1794.767
## 1935                      217.1512                      1794.767
## 1936                      217.1512                      1794.767
## 1937                      217.1512                      1794.767
## 1938                      217.1512                      1794.767
## 1939                      217.1512                      1794.767
## 1940                      217.1512                      1794.767
## 1941                      217.1512                      1794.767
## 1942                      217.1512                      1794.767
## 1943                      217.1512                      1794.767
## 1944                      217.1512                      1794.767
## 1945                     1473.8372                      7573.256
## 1946                     1473.8372                      7573.256
## 1947                     1473.8372                      7573.256
## 1948                     1473.8372                      7573.256
## 1949                     1473.8372                      7573.256
## 1950                     1473.8372                      7573.256
## 1951                     1473.8372                      7573.256
## 1952                     1473.8372                      7573.256
## 1953                     1473.8372                      7573.256
## 1954                     1473.8372                      7573.256
## 1955                     1473.8372                      7573.256
## 1956                     1473.8372                      7573.256
## 1957                     1473.8372                      7573.256
## 1958                     1473.8372                      7573.256
## 1959                     1473.8372                      7573.256
## 1960                     1473.8372                      7573.256
## 1961                     1473.8372                      7573.256
## 1962                     1473.8372                      7573.256
## 1963                     1473.8372                      7573.256
## 1964                     1473.8372                      7573.256
## 1965                     1473.8372                      7573.256
## 1966                     1473.8372                      7573.256
## 1967                     1473.8372                      7573.256
## 1968                     1473.8372                      7573.256
## 1969                     2502.9070                     11834.302
## 1970                     2502.9070                     11834.302
## 1971                     2502.9070                     11834.302
## 1972                     2502.9070                     11834.302
## 1973                     2502.9070                     11834.302
## 1974                     2502.9070                     11834.302
## 1975                     2502.9070                     11834.302
## 1976                     2502.9070                     11834.302
## 1977                     2502.9070                     11834.302
## 1978                     2502.9070                     11834.302
## 1979                     2502.9070                     11834.302
## 1980                     2502.9070                     11834.302
## 1981                     2502.9070                     11834.302
## 1982                     2502.9070                     11834.302
## 1983                     2502.9070                     11834.302
## 1984                     2502.9070                     11834.302
## 1985                     2502.9070                     11834.302
## 1986                     2502.9070                     11834.302
## 1987                     2502.9070                     11834.302
## 1988                     2502.9070                     11834.302
## 1989                     2502.9070                     11834.302
## 1990                     2502.9070                     11834.302
## 1991                     2502.9070                     11834.302
## 1992                     2502.9070                     11834.302
## 1993                     3388.9535                      8497.674
## 1994                     3388.9535                      8497.674
## 1995                     3388.9535                      8497.674
## 1996                     3388.9535                      8497.674
## 1997                     3388.9535                      8497.674
## 1998                     3388.9535                      8497.674
## 1999                     3388.9535                      8497.674
## 2000                     3388.9535                      8497.674
## 2001                     3388.9535                      8497.674
## 2002                     3388.9535                      8497.674
## 2003                     3388.9535                      8497.674
## 2004                     3388.9535                      8497.674
## 2005                     3388.9535                      8497.674
## 2006                     3388.9535                      8497.674
## 2007                     3388.9535                      8497.674
## 2008                     3388.9535                      8497.674
## 2009                     3388.9535                      8497.674
## 2010                     3388.9535                      8497.674
## 2011                     3388.9535                      8497.674
## 2012                     3388.9535                      8497.674
## 2013                     3388.9535                      8497.674
## 2014                     3388.9535                      8497.674
## 2015                     3388.9535                      8497.674
## 2016                     3388.9535                      8497.674
## 2017                     3584.3023                      9950.581
## 2018                     3584.3023                      9950.581
## 2019                     3584.3023                      9950.581
## 2020                     3584.3023                      9950.581
## 2021                     3584.3023                      9950.581
## 2022                     3584.3023                      9950.581
## 2023                     3584.3023                      9950.581
## 2024                     3584.3023                      9950.581
## 2025                     3584.3023                      9950.581
## 2026                     3584.3023                      9950.581
## 2027                     3584.3023                      9950.581
## 2028                     3584.3023                      9950.581
## 2029                     3584.3023                      9950.581
## 2030                     3584.3023                      9950.581
## 2031                     3584.3023                      9950.581
## 2032                     3584.3023                      9950.581
## 2033                     3584.3023                      9950.581
## 2034                     3584.3023                      9950.581
## 2035                     3584.3023                      9950.581
## 2036                     3584.3023                      9950.581
## 2037                     3584.3023                      9950.581
## 2038                     3584.3023                      9950.581
## 2039                     3584.3023                      9950.581
## 2040                     3584.3023                      9950.581
## 2041                     3750.0000                      9680.233
## 2042                     3750.0000                      9680.233
## 2043                     3750.0000                      9680.233
## 2044                     3750.0000                      9680.233
## 2045                     3750.0000                      9680.233
## 2046                     3750.0000                      9680.233
## 2047                     3750.0000                      9680.233
## 2048                     3750.0000                      9680.233
## 2049                     3750.0000                      9680.233
## 2050                     3750.0000                      9680.233
## 2051                     3750.0000                      9680.233
## 2052                     3750.0000                      9680.233
## 2053                     3750.0000                      9680.233
## 2054                     3750.0000                      9680.233
## 2055                     3750.0000                      9680.233
## 2056                     3750.0000                      9680.233
## 2057                     3750.0000                      9680.233
## 2058                     3750.0000                      9680.233
## 2059                     3750.0000                      9680.233
## 2060                     3750.0000                      9680.233
## 2061                     3750.0000                      9680.233
## 2062                     3750.0000                      9680.233
## 2063                     3750.0000                      9680.233
## 2064                     3750.0000                      9680.233
## 2065                     2768.8953                     15496.221
## 2066                     2768.8953                     15496.221
## 2067                     2768.8953                     15496.221
## 2068                     2768.8953                     15496.221
## 2069                     2768.8953                     15496.221
## 2070                     2768.8953                     15496.221
## 2071                     2768.8953                     15496.221
## 2072                     2768.8953                     15496.221
## 2073                     2768.8953                     15496.221
## 2074                     2768.8953                     15496.221
## 2075                     2768.8953                     15496.221
## 2076                     2768.8953                     15496.221
## 2077                     2768.8953                     15496.221
## 2078                     2768.8953                     15496.221
## 2079                     2768.8953                     15496.221
## 2080                     2768.8953                     15496.221
## 2081                     2768.8953                     15496.221
## 2082                     2768.8953                     15496.221
## 2083                     2768.8953                     15496.221
## 2084                     2768.8953                     15496.221
## 2085                     2768.8953                     15496.221
## 2086                     2768.8953                     15496.221
## 2087                     2768.8953                     15496.221
## 2088                     2768.8953                     15496.221
## 2089                     1748.5465                     15620.930
## 2090                     1748.5465                     15620.930
## 2091                     1748.5465                     15620.930
## 2092                     1748.5465                     15620.930
## 2093                     1748.5465                     15620.930
## 2094                     1748.5465                     15620.930
## 2095                     1748.5465                     15620.930
## 2096                     1748.5465                     15620.930
## 2097                     1748.5465                     15620.930
## 2098                     1748.5465                     15620.930
## 2099                     1748.5465                     15620.930
## 2100                     1748.5465                     15620.930
## 2101                     1748.5465                     15620.930
## 2102                     1748.5465                     15620.930
## 2103                     1748.5465                     15620.930
## 2104                     1748.5465                     15620.930
## 2105                     1748.5465                     15620.930
## 2106                     1748.5465                     15620.930
## 2107                     1748.5465                     15620.930
## 2108                     1748.5465                     15620.930
## 2109                     1748.5465                     15620.930
## 2110                     1748.5465                     15620.930
## 2111                     1748.5465                     15620.930
## 2112                     1748.5465                     15620.930
## 2113                      217.1512                      1794.767
## 2114                      217.1512                      1794.767
## 2115                      217.1512                      1794.767
## 2116                      217.1512                      1794.767
## 2117                      217.1512                      1794.767
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## 2305                      217.1512                      1794.767
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## 2497                      217.1512                      1794.767
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## 2508                      217.1512                      1794.767
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## 3137                     2879.6512                     12280.814
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## 3139                     2879.6512                     12280.814
## 3140                     2879.6512                     12280.814
## 3141                     2879.6512                     12280.814
## 3142                     2879.6512                     12280.814
## 3143                     2879.6512                     12280.814
## 3144                     2879.6512                     12280.814
## 3145                     4534.8837                     15790.116
## 3146                     4534.8837                     15790.116
## 3147                     4534.8837                     15790.116
## 3148                     4534.8837                     15790.116
## 3149                     4534.8837                     15790.116
## 3150                     4534.8837                     15790.116
## 3151                     4534.8837                     15790.116
## 3152                     4534.8837                     15790.116
## 3153                     4534.8837                     15790.116
## 3154                     4534.8837                     15790.116
## 3155                     4534.8837                     15790.116
## 3156                     4534.8837                     15790.116
## 3157                     4534.8837                     15790.116
## 3158                     4534.8837                     15790.116
## 3159                     4534.8837                     15790.116
## 3160                     4534.8837                     15790.116
## 3161                     4534.8837                     15790.116
## 3162                     4534.8837                     15790.116
## 3163                     4534.8837                     15790.116
## 3164                     4534.8837                     15790.116
## 3165                     4534.8837                     15790.116
## 3166                     4534.8837                     15790.116
## 3167                     4534.8837                     15790.116
## 3168                     4534.8837                     15790.116
## 3169                     3226.7442                     12861.628
## 3170                     3226.7442                     12861.628
## 3171                     3226.7442                     12861.628
## 3172                     3226.7442                     12861.628
## 3173                     3226.7442                     12861.628
## 3174                     3226.7442                     12861.628
## 3175                     3226.7442                     12861.628
## 3176                     3226.7442                     12861.628
## 3177                     3226.7442                     12861.628
## 3178                     3226.7442                     12861.628
## 3179                     3226.7442                     12861.628
## 3180                     3226.7442                     12861.628
## 3181                     3226.7442                     12861.628
## 3182                     3226.7442                     12861.628
## 3183                     3226.7442                     12861.628
## 3184                     3226.7442                     12861.628
## 3185                     3226.7442                     12861.628
## 3186                     3226.7442                     12861.628
## 3187                     3226.7442                     12861.628
## 3188                     3226.7442                     12861.628
## 3189                     3226.7442                     12861.628
## 3190                     3226.7442                     12861.628
## 3191                     3226.7442                     12861.628
## 3192                     3226.7442                     12861.628
## 3193                     2659.8837                      7986.628
## 3194                     2659.8837                      7986.628
## 3195                     2659.8837                      7986.628
## 3196                     2659.8837                      7986.628
## 3197                     2659.8837                      7986.628
## 3198                     2659.8837                      7986.628
## 3199                     2659.8837                      7986.628
## 3200                     2659.8837                      7986.628
## 3201                     2659.8837                      7986.628
## 3202                     2659.8837                      7986.628
## 3203                     2659.8837                      7986.628
## 3204                     2659.8837                      7986.628
## 3205                     2659.8837                      7986.628
## 3206                     2659.8837                      7986.628
## 3207                     2659.8837                      7986.628
## 3208                     2659.8837                      7986.628
## 3209                     2659.8837                      7986.628
## 3210                     2659.8837                      7986.628
## 3211                     2659.8837                      7986.628
## 3212                     2659.8837                      7986.628
## 3213                     2659.8837                      7986.628
## 3214                     2659.8837                      7986.628
## 3215                     2659.8837                      7986.628
## 3216                     2659.8837                      7986.628
## 3217                     4765.9884                     12342.733
## 3218                     4765.9884                     12342.733
## 3219                     4765.9884                     12342.733
## 3220                     4765.9884                     12342.733
## 3221                     4765.9884                     12342.733
## 3222                     4765.9884                     12342.733
## 3223                     4765.9884                     12342.733
## 3224                     4765.9884                     12342.733
## 3225                     4765.9884                     12342.733
##      total_metaecosystem_Col_indiv total_metaecosystem_Eug_indiv
## 1                       4812.20930                    7834.88372
## 2                       4812.20930                    7834.88372
## 3                       4812.20930                    7834.88372
## 4                       4812.20930                    7834.88372
## 5                       4812.20930                    7834.88372
## 6                       4812.20930                    7834.88372
## 7                       4812.20930                    7834.88372
## 8                       4812.20930                    7834.88372
## 9                       4812.20930                    7834.88372
## 10                      4812.20930                    7834.88372
## 11                      4812.20930                    7834.88372
## 12                      4812.20930                    7834.88372
## 13                      4812.20930                    7834.88372
## 14                      4812.20930                    7834.88372
## 15                      4812.20930                    7834.88372
## 16                      4812.20930                    7834.88372
## 17                      4812.20930                    7834.88372
## 18                      4812.20930                    7834.88372
## 19                      4812.20930                    7834.88372
## 20                      4812.20930                    7834.88372
## 21                      4812.20930                    7834.88372
## 22                      4812.20930                    7834.88372
## 23                      4812.20930                    7834.88372
## 24                      4812.20930                    7834.88372
## 25                     20305.81395                    3057.55814
## 26                     20305.81395                    3057.55814
## 27                     20305.81395                    3057.55814
## 28                     20305.81395                    3057.55814
## 29                     20305.81395                    3057.55814
## 30                     20305.81395                    3057.55814
## 31                     20305.81395                    3057.55814
## 32                     20305.81395                    3057.55814
## 33                     20305.81395                    3057.55814
## 34                     20305.81395                    3057.55814
## 35                     20305.81395                    3057.55814
## 36                     20305.81395                    3057.55814
## 37                     20305.81395                    3057.55814
## 38                     20305.81395                    3057.55814
## 39                     20305.81395                    3057.55814
## 40                     20305.81395                    3057.55814
## 41                     20305.81395                    3057.55814
## 42                     20305.81395                    3057.55814
## 43                     20305.81395                    3057.55814
## 44                     20305.81395                    3057.55814
## 45                     20305.81395                    3057.55814
## 46                     20305.81395                    3057.55814
## 47                     20305.81395                    3057.55814
## 48                     20305.81395                    3057.55814
## 49                     16356.97674                     218.02326
## 50                     16356.97674                     218.02326
## 51                     16356.97674                     218.02326
## 52                     16356.97674                     218.02326
## 53                     16356.97674                     218.02326
## 54                     16356.97674                     218.02326
## 55                     16356.97674                     218.02326
## 56                     16356.97674                     218.02326
## 57                     16356.97674                     218.02326
## 58                     16356.97674                     218.02326
## 59                     16356.97674                     218.02326
## 60                     16356.97674                     218.02326
## 61                     16356.97674                     218.02326
## 62                     16356.97674                     218.02326
## 63                     16356.97674                     218.02326
## 64                     16356.97674                     218.02326
## 65                     16356.97674                     218.02326
## 66                     16356.97674                     218.02326
## 67                     16356.97674                     218.02326
## 68                     16356.97674                     218.02326
## 69                     16356.97674                     218.02326
## 70                     16356.97674                     218.02326
## 71                     16356.97674                     218.02326
## 72                     16356.97674                     218.02326
## 73                      6973.25581                       0.00000
## 74                      6973.25581                       0.00000
## 75                      6973.25581                       0.00000
## 76                      6973.25581                       0.00000
## 77                      6973.25581                       0.00000
## 78                      6973.25581                       0.00000
## 79                      6973.25581                       0.00000
## 80                      6973.25581                       0.00000
## 81                      6973.25581                       0.00000
## 82                      6973.25581                       0.00000
## 83                      6973.25581                       0.00000
## 84                      6973.25581                       0.00000
## 85                      6973.25581                       0.00000
## 86                      6973.25581                       0.00000
## 87                      6973.25581                       0.00000
## 88                      6973.25581                       0.00000
## 89                      6973.25581                       0.00000
## 90                      6973.25581                       0.00000
## 91                      6973.25581                       0.00000
## 92                      6973.25581                       0.00000
## 93                      6973.25581                       0.00000
## 94                      6973.25581                       0.00000
## 95                      6973.25581                       0.00000
## 96                      6973.25581                       0.00000
## 97                      3912.20930                       0.00000
## 98                      3912.20930                       0.00000
## 99                      3912.20930                       0.00000
## 100                     3912.20930                       0.00000
## 101                     3912.20930                       0.00000
## 102                     3912.20930                       0.00000
## 103                     3912.20930                       0.00000
## 104                     3912.20930                       0.00000
## 105                     3912.20930                       0.00000
## 106                     3912.20930                       0.00000
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## 114                     3912.20930                       0.00000
## 115                     3912.20930                       0.00000
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## 118                     3912.20930                       0.00000
## 119                     3912.20930                       0.00000
## 120                     3912.20930                       0.00000
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## 129                        0.00000                       0.00000
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## 132                        0.00000                       0.00000
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## 162                      418.60465                       0.00000
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## 165                      418.60465                       0.00000
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## 167                      418.60465                       0.00000
## 168                      418.60465                       0.00000
## 169                        0.00000                    1090.11628
## 170                        0.00000                    1090.11628
## 171                        0.00000                    1090.11628
## 172                        0.00000                    1090.11628
## 173                        0.00000                    1090.11628
## 174                        0.00000                    1090.11628
## 175                        0.00000                    1090.11628
## 176                        0.00000                    1090.11628
## 177                        0.00000                    1090.11628
## 178                        0.00000                    1090.11628
## 179                        0.00000                    1090.11628
## 180                        0.00000                    1090.11628
## 181                        0.00000                    1090.11628
## 182                        0.00000                    1090.11628
## 183                        0.00000                    1090.11628
## 184                        0.00000                    1090.11628
## 185                        0.00000                    1090.11628
## 186                        0.00000                    1090.11628
## 187                        0.00000                    1090.11628
## 188                        0.00000                    1090.11628
## 189                        0.00000                    1090.11628
## 190                        0.00000                    1090.11628
## 191                        0.00000                    1090.11628
## 192                        0.00000                    1090.11628
## 193                     4812.20930                    7834.88372
## 194                     4812.20930                    7834.88372
## 195                     4812.20930                    7834.88372
## 196                     4812.20930                    7834.88372
## 197                     4812.20930                    7834.88372
## 198                     4812.20930                    7834.88372
## 199                     4812.20930                    7834.88372
## 200                     4812.20930                    7834.88372
## 201                     4812.20930                    7834.88372
## 202                     4812.20930                    7834.88372
## 203                     4812.20930                    7834.88372
## 204                     4812.20930                    7834.88372
## 205                     4812.20930                    7834.88372
## 206                     4812.20930                    7834.88372
## 207                     4812.20930                    7834.88372
## 208                     4812.20930                    7834.88372
## 209                     4812.20930                    7834.88372
## 210                     4812.20930                    7834.88372
## 211                     4812.20930                    7834.88372
## 212                     4812.20930                    7834.88372
## 213                     4812.20930                    7834.88372
## 214                     4812.20930                    7834.88372
## 215                     4812.20930                    7834.88372
## 216                     4812.20930                    7834.88372
## 217                    12404.65116                    1941.27907
## 218                    12404.65116                    1941.27907
## 219                    12404.65116                    1941.27907
## 220                    12404.65116                    1941.27907
## 221                    12404.65116                    1941.27907
## 222                    12404.65116                    1941.27907
## 223                    12404.65116                    1941.27907
## 224                    12404.65116                    1941.27907
## 225                    12404.65116                    1941.27907
## 226                    12404.65116                    1941.27907
## 227                    12404.65116                    1941.27907
## 228                    12404.65116                    1941.27907
## 229                    12404.65116                    1941.27907
## 230                    12404.65116                    1941.27907
## 231                    12404.65116                    1941.27907
## 232                    12404.65116                    1941.27907
## 233                    12404.65116                    1941.27907
## 234                    12404.65116                    1941.27907
## 235                    12404.65116                    1941.27907
## 236                    12404.65116                    1941.27907
## 237                    12404.65116                    1941.27907
## 238                    12404.65116                    1941.27907
## 239                    12404.65116                    1941.27907
## 240                    12404.65116                    1941.27907
## 241                     5159.30233                     218.02326
## 242                     5159.30233                     218.02326
## 243                     5159.30233                     218.02326
## 244                     5159.30233                     218.02326
## 245                     5159.30233                     218.02326
## 246                     5159.30233                     218.02326
## 247                     5159.30233                     218.02326
## 248                     5159.30233                     218.02326
## 249                     5159.30233                     218.02326
## 250                     5159.30233                     218.02326
## 251                     5159.30233                     218.02326
## 252                     5159.30233                     218.02326
## 253                     5159.30233                     218.02326
## 254                     5159.30233                     218.02326
## 255                     5159.30233                     218.02326
## 256                     5159.30233                     218.02326
## 257                     5159.30233                     218.02326
## 258                     5159.30233                     218.02326
## 259                     5159.30233                     218.02326
## 260                     5159.30233                     218.02326
## 261                     5159.30233                     218.02326
## 262                     5159.30233                     218.02326
## 263                     5159.30233                     218.02326
## 264                     5159.30233                     218.02326
## 265                     3685.46512                    1438.95349
## 266                     3685.46512                    1438.95349
## 267                     3685.46512                    1438.95349
## 268                     3685.46512                    1438.95349
## 269                     3685.46512                    1438.95349
## 270                     3685.46512                    1438.95349
## 271                     3685.46512                    1438.95349
## 272                     3685.46512                    1438.95349
## 273                     3685.46512                    1438.95349
## 274                     3685.46512                    1438.95349
## 275                     3685.46512                    1438.95349
## 276                     3685.46512                    1438.95349
## 277                     3685.46512                    1438.95349
## 278                     3685.46512                    1438.95349
## 279                     3685.46512                    1438.95349
## 280                     3685.46512                    1438.95349
## 281                     3685.46512                    1438.95349
## 282                     3685.46512                    1438.95349
## 283                     3685.46512                    1438.95349
## 284                     3685.46512                    1438.95349
## 285                     3685.46512                    1438.95349
## 286                     3685.46512                    1438.95349
## 287                     3685.46512                    1438.95349
## 288                     3685.46512                    1438.95349
## 289                      397.67442                       0.00000
## 290                      397.67442                       0.00000
## 291                      397.67442                       0.00000
## 292                      397.67442                       0.00000
## 293                      397.67442                       0.00000
## 294                      397.67442                       0.00000
## 295                      397.67442                       0.00000
## 296                      397.67442                       0.00000
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## 300                      397.67442                       0.00000
## 301                      397.67442                       0.00000
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## 305                      397.67442                       0.00000
## 306                      397.67442                       0.00000
## 307                      397.67442                       0.00000
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## 309                      397.67442                       0.00000
## 310                      397.67442                       0.00000
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## 313                      837.20930                       0.00000
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## 315                      837.20930                       0.00000
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## 319                      837.20930                       0.00000
## 320                      837.20930                       0.00000
## 321                      837.20930                       0.00000
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## 323                      837.20930                       0.00000
## 324                      837.20930                       0.00000
## 325                      837.20930                       0.00000
## 326                      837.20930                       0.00000
## 327                      837.20930                       0.00000
## 328                      837.20930                       0.00000
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## 331                      837.20930                       0.00000
## 332                      837.20930                       0.00000
## 333                      837.20930                       0.00000
## 334                      837.20930                       0.00000
## 335                      837.20930                       0.00000
## 336                      837.20930                       0.00000
## 337                        0.00000                    1312.50000
## 338                        0.00000                    1312.50000
## 339                        0.00000                    1312.50000
## 340                        0.00000                    1312.50000
## 341                        0.00000                    1312.50000
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## 356                        0.00000                    1312.50000
## 357                        0.00000                    1312.50000
## 358                        0.00000                    1312.50000
## 359                        0.00000                    1312.50000
## 360                        0.00000                    1312.50000
## 361                        0.00000                    1962.20930
## 362                        0.00000                    1962.20930
## 363                        0.00000                    1962.20930
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## 387                     4812.20930                    7834.88372
## 388                     4812.20930                    7834.88372
## 389                     4812.20930                    7834.88372
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## 395                     4812.20930                    7834.88372
## 396                     4812.20930                    7834.88372
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## 399                     4812.20930                    7834.88372
## 400                     4812.20930                    7834.88372
## 401                     4812.20930                    7834.88372
## 402                     4812.20930                    7834.88372
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## 404                     4812.20930                    7834.88372
## 405                     4812.20930                    7834.88372
## 406                     4812.20930                    7834.88372
## 407                     4812.20930                    7834.88372
## 408                     4812.20930                    7834.88372
## 409                    17236.04651                    2263.95349
## 410                    17236.04651                    2263.95349
## 411                    17236.04651                    2263.95349
## 412                    17236.04651                    2263.95349
## 413                    17236.04651                    2263.95349
## 414                    17236.04651                    2263.95349
## 415                    17236.04651                    2263.95349
## 416                    17236.04651                    2263.95349
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## 420                    17236.04651                    2263.95349
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## 422                    17236.04651                    2263.95349
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## 425                    17236.04651                    2263.95349
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## 430                    17236.04651                    2263.95349
## 431                    17236.04651                    2263.95349
## 432                    17236.04651                    2263.95349
## 433                     6022.67442                     218.02326
## 434                     6022.67442                     218.02326
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## 459                     4060.46512                     837.20930
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## 2019                    3514.53488                     650.58140
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## 3122                    5752.32558                     127.32558
## 3123                    5752.32558                     127.32558
## 3124                    5752.32558                     127.32558
## 3125                    5752.32558                     127.32558
## 3126                    5752.32558                     127.32558
## 3127                    5752.32558                     127.32558
## 3128                    5752.32558                     127.32558
## 3129                    5752.32558                     127.32558
## 3130                    5752.32558                     127.32558
## 3131                    5752.32558                     127.32558
## 3132                    5752.32558                     127.32558
## 3133                    5752.32558                     127.32558
## 3134                    5752.32558                     127.32558
## 3135                    5752.32558                     127.32558
## 3136                    5752.32558                     127.32558
## 3137                    5752.32558                     127.32558
## 3138                    5752.32558                     127.32558
## 3139                    5752.32558                     127.32558
## 3140                    5752.32558                     127.32558
## 3141                    5752.32558                     127.32558
## 3142                    5752.32558                     127.32558
## 3143                    5752.32558                     127.32558
## 3144                    5752.32558                     127.32558
## 3145                    4046.51163                    1438.95349
## 3146                    4046.51163                    1438.95349
## 3147                    4046.51163                    1438.95349
## 3148                    4046.51163                    1438.95349
## 3149                    4046.51163                    1438.95349
## 3150                    4046.51163                    1438.95349
## 3151                    4046.51163                    1438.95349
## 3152                    4046.51163                    1438.95349
## 3153                    4046.51163                    1438.95349
## 3154                    4046.51163                    1438.95349
## 3155                    4046.51163                    1438.95349
## 3156                    4046.51163                    1438.95349
## 3157                    4046.51163                    1438.95349
## 3158                    4046.51163                    1438.95349
## 3159                    4046.51163                    1438.95349
## 3160                    4046.51163                    1438.95349
## 3161                    4046.51163                    1438.95349
## 3162                    4046.51163                    1438.95349
## 3163                    4046.51163                    1438.95349
## 3164                    4046.51163                    1438.95349
## 3165                    4046.51163                    1438.95349
## 3166                    4046.51163                    1438.95349
## 3167                    4046.51163                    1438.95349
## 3168                    4046.51163                    1438.95349
## 3169                     568.60465                       0.00000
## 3170                     568.60465                       0.00000
## 3171                     568.60465                       0.00000
## 3172                     568.60465                       0.00000
## 3173                     568.60465                       0.00000
## 3174                     568.60465                       0.00000
## 3175                     568.60465                       0.00000
## 3176                     568.60465                       0.00000
## 3177                     568.60465                       0.00000
## 3178                     568.60465                       0.00000
## 3179                     568.60465                       0.00000
## 3180                     568.60465                       0.00000
## 3181                     568.60465                       0.00000
## 3182                     568.60465                       0.00000
## 3183                     568.60465                       0.00000
## 3184                     568.60465                       0.00000
## 3185                     568.60465                       0.00000
## 3186                     568.60465                       0.00000
## 3187                     568.60465                       0.00000
## 3188                     568.60465                       0.00000
## 3189                     568.60465                       0.00000
## 3190                     568.60465                       0.00000
## 3191                     568.60465                       0.00000
## 3192                     568.60465                       0.00000
## 3193                     837.20930                       0.00000
## 3194                     837.20930                       0.00000
## 3195                     837.20930                       0.00000
## 3196                     837.20930                       0.00000
## 3197                     837.20930                       0.00000
## 3198                     837.20930                       0.00000
## 3199                     837.20930                       0.00000
## 3200                     837.20930                       0.00000
## 3201                     837.20930                       0.00000
## 3202                     837.20930                       0.00000
## 3203                     837.20930                       0.00000
## 3204                     837.20930                       0.00000
## 3205                     837.20930                       0.00000
## 3206                     837.20930                       0.00000
## 3207                     837.20930                       0.00000
## 3208                     837.20930                       0.00000
## 3209                     837.20930                       0.00000
## 3210                     837.20930                       0.00000
## 3211                     837.20930                       0.00000
## 3212                     837.20930                       0.00000
## 3213                     837.20930                       0.00000
## 3214                     837.20930                       0.00000
## 3215                     837.20930                       0.00000
## 3216                     837.20930                       0.00000
## 3217                       0.00000                    1312.50000
## 3218                       0.00000                    1312.50000
## 3219                       0.00000                    1312.50000
## 3220                       0.00000                    1312.50000
## 3221                       0.00000                    1312.50000
## 3222                       0.00000                    1312.50000
## 3223                       0.00000                    1312.50000
## 3224                       0.00000                    1312.50000
## 3225                       0.00000                    1312.50000
##      total_metaecosystem_Eup_indiv total_metaecosystem_Lox_indiv
## 1                        3155.2326                     2494.1860
## 2                        3155.2326                     2494.1860
## 3                        3155.2326                     2494.1860
## 4                        3155.2326                     2494.1860
## 5                        3155.2326                     2494.1860
## 6                        3155.2326                     2494.1860
## 7                        3155.2326                     2494.1860
## 8                        3155.2326                     2494.1860
## 9                        3155.2326                     2494.1860
## 10                       3155.2326                     2494.1860
## 11                       3155.2326                     2494.1860
## 12                       3155.2326                     2494.1860
## 13                       3155.2326                     2494.1860
## 14                       3155.2326                     2494.1860
## 15                       3155.2326                     2494.1860
## 16                       3155.2326                     2494.1860
## 17                       3155.2326                     2494.1860
## 18                       3155.2326                     2494.1860
## 19                       3155.2326                     2494.1860
## 20                       3155.2326                     2494.1860
## 21                       3155.2326                     2494.1860
## 22                       3155.2326                     2494.1860
## 23                       3155.2326                     2494.1860
## 24                       3155.2326                     2494.1860
## 25                       4484.3023                      218.0233
## 26                       4484.3023                      218.0233
## 27                       4484.3023                      218.0233
## 28                       4484.3023                      218.0233
## 29                       4484.3023                      218.0233
## 30                       4484.3023                      218.0233
## 31                       4484.3023                      218.0233
## 32                       4484.3023                      218.0233
## 33                       4484.3023                      218.0233
## 34                       4484.3023                      218.0233
## 35                       4484.3023                      218.0233
## 36                       4484.3023                      218.0233
## 37                       4484.3023                      218.0233
## 38                       4484.3023                      218.0233
## 39                       4484.3023                      218.0233
## 40                       4484.3023                      218.0233
## 41                       4484.3023                      218.0233
## 42                       4484.3023                      218.0233
## 43                       4484.3023                      218.0233
## 44                       4484.3023                      218.0233
## 45                       4484.3023                      218.0233
## 46                       4484.3023                      218.0233
## 47                       4484.3023                      218.0233
## 48                       4484.3023                      218.0233
## 49                       1318.6047                        0.0000
## 50                       1318.6047                        0.0000
## 51                       1318.6047                        0.0000
## 52                       1318.6047                        0.0000
## 53                       1318.6047                        0.0000
## 54                       1318.6047                        0.0000
## 55                       1318.6047                        0.0000
## 56                       1318.6047                        0.0000
## 57                       1318.6047                        0.0000
## 58                       1318.6047                        0.0000
## 59                       1318.6047                        0.0000
## 60                       1318.6047                        0.0000
## 61                       1318.6047                        0.0000
## 62                       1318.6047                        0.0000
## 63                       1318.6047                        0.0000
## 64                       1318.6047                        0.0000
## 65                       1318.6047                        0.0000
## 66                       1318.6047                        0.0000
## 67                       1318.6047                        0.0000
## 68                       1318.6047                        0.0000
## 69                       1318.6047                        0.0000
## 70                       1318.6047                        0.0000
## 71                       1318.6047                        0.0000
## 72                       1318.6047                        0.0000
## 73                       5084.3023                        0.0000
## 74                       5084.3023                        0.0000
## 75                       5084.3023                        0.0000
## 76                       5084.3023                        0.0000
## 77                       5084.3023                        0.0000
## 78                       5084.3023                        0.0000
## 79                       5084.3023                        0.0000
## 80                       5084.3023                        0.0000
## 81                       5084.3023                        0.0000
## 82                       5084.3023                        0.0000
## 83                       5084.3023                        0.0000
## 84                       5084.3023                        0.0000
## 85                       5084.3023                        0.0000
## 86                       5084.3023                        0.0000
## 87                       5084.3023                        0.0000
## 88                       5084.3023                        0.0000
## 89                       5084.3023                        0.0000
## 90                       5084.3023                        0.0000
## 91                       5084.3023                        0.0000
## 92                       5084.3023                        0.0000
## 93                       5084.3023                        0.0000
## 94                       5084.3023                        0.0000
## 95                       5084.3023                        0.0000
## 96                       5084.3023                        0.0000
## 97                       5241.2791                      436.0465
## 98                       5241.2791                      436.0465
## 99                       5241.2791                      436.0465
## 100                      5241.2791                      436.0465
## 101                      5241.2791                      436.0465
## 102                      5241.2791                      436.0465
## 103                      5241.2791                      436.0465
## 104                      5241.2791                      436.0465
## 105                      5241.2791                      436.0465
## 106                      5241.2791                      436.0465
## 107                      5241.2791                      436.0465
## 108                      5241.2791                      436.0465
## 109                      5241.2791                      436.0465
## 110                      5241.2791                      436.0465
## 111                      5241.2791                      436.0465
## 112                      5241.2791                      436.0465
## 113                      5241.2791                      436.0465
## 114                      5241.2791                      436.0465
## 115                      5241.2791                      436.0465
## 116                      5241.2791                      436.0465
## 117                      5241.2791                      436.0465
## 118                      5241.2791                      436.0465
## 119                      5241.2791                      436.0465
## 120                      5241.2791                      436.0465
## 121                      2956.3953                        0.0000
## 122                      2956.3953                        0.0000
## 123                      2956.3953                        0.0000
## 124                      2956.3953                        0.0000
## 125                      2956.3953                        0.0000
## 126                      2956.3953                        0.0000
## 127                      2956.3953                        0.0000
## 128                      2956.3953                        0.0000
## 129                      2956.3953                        0.0000
## 130                      2956.3953                        0.0000
## 131                      2956.3953                        0.0000
## 132                      2956.3953                        0.0000
## 133                      2956.3953                        0.0000
## 134                      2956.3953                        0.0000
## 135                      2956.3953                        0.0000
## 136                      2956.3953                        0.0000
## 137                      2956.3953                        0.0000
## 138                      2956.3953                        0.0000
## 139                      2956.3953                        0.0000
## 140                      2956.3953                        0.0000
## 141                      2956.3953                        0.0000
## 142                      2956.3953                        0.0000
## 143                      2956.3953                        0.0000
## 144                      2956.3953                        0.0000
## 145                       662.7907                      545.0581
## 146                       662.7907                      545.0581
## 147                       662.7907                      545.0581
## 148                       662.7907                      545.0581
## 149                       662.7907                      545.0581
## 150                       662.7907                      545.0581
## 151                       662.7907                      545.0581
## 152                       662.7907                      545.0581
## 153                       662.7907                      545.0581
## 154                       662.7907                      545.0581
## 155                       662.7907                      545.0581
## 156                       662.7907                      545.0581
## 157                       662.7907                      545.0581
## 158                       662.7907                      545.0581
## 159                       662.7907                      545.0581
## 160                       662.7907                      545.0581
## 161                       662.7907                      545.0581
## 162                       662.7907                      545.0581
## 163                       662.7907                      545.0581
## 164                       662.7907                      545.0581
## 165                       662.7907                      545.0581
## 166                       662.7907                      545.0581
## 167                       662.7907                      545.0581
## 168                       662.7907                      545.0581
## 169                      2428.7791                     1630.8140
## 170                      2428.7791                     1630.8140
## 171                      2428.7791                     1630.8140
## 172                      2428.7791                     1630.8140
## 173                      2428.7791                     1630.8140
## 174                      2428.7791                     1630.8140
## 175                      2428.7791                     1630.8140
## 176                      2428.7791                     1630.8140
## 177                      2428.7791                     1630.8140
## 178                      2428.7791                     1630.8140
## 179                      2428.7791                     1630.8140
## 180                      2428.7791                     1630.8140
## 181                      2428.7791                     1630.8140
## 182                      2428.7791                     1630.8140
## 183                      2428.7791                     1630.8140
## 184                      2428.7791                     1630.8140
## 185                      2428.7791                     1630.8140
## 186                      2428.7791                     1630.8140
## 187                      2428.7791                     1630.8140
## 188                      2428.7791                     1630.8140
## 189                      2428.7791                     1630.8140
## 190                      2428.7791                     1630.8140
## 191                      2428.7791                     1630.8140
## 192                      2428.7791                     1630.8140
## 193                      3155.2326                     2494.1860
## 194                      3155.2326                     2494.1860
## 195                      3155.2326                     2494.1860
## 196                      3155.2326                     2494.1860
## 197                      3155.2326                     2494.1860
## 198                      3155.2326                     2494.1860
## 199                      3155.2326                     2494.1860
## 200                      3155.2326                     2494.1860
## 201                      3155.2326                     2494.1860
## 202                      3155.2326                     2494.1860
## 203                      3155.2326                     2494.1860
## 204                      3155.2326                     2494.1860
## 205                      3155.2326                     2494.1860
## 206                      3155.2326                     2494.1860
## 207                      3155.2326                     2494.1860
## 208                      3155.2326                     2494.1860
## 209                      3155.2326                     2494.1860
## 210                      3155.2326                     2494.1860
## 211                      3155.2326                     2494.1860
## 212                      3155.2326                     2494.1860
## 213                      3155.2326                     2494.1860
## 214                      3155.2326                     2494.1860
## 215                      3155.2326                     2494.1860
## 216                      3155.2326                     2494.1860
## 217                      8312.7907                     1438.9535
## 218                      8312.7907                     1438.9535
## 219                      8312.7907                     1438.9535
## 220                      8312.7907                     1438.9535
## 221                      8312.7907                     1438.9535
## 222                      8312.7907                     1438.9535
## 223                      8312.7907                     1438.9535
## 224                      8312.7907                     1438.9535
## 225                      8312.7907                     1438.9535
## 226                      8312.7907                     1438.9535
## 227                      8312.7907                     1438.9535
## 228                      8312.7907                     1438.9535
## 229                      8312.7907                     1438.9535
## 230                      8312.7907                     1438.9535
## 231                      8312.7907                     1438.9535
## 232                      8312.7907                     1438.9535
## 233                      8312.7907                     1438.9535
## 234                      8312.7907                     1438.9535
## 235                      8312.7907                     1438.9535
## 236                      8312.7907                     1438.9535
## 237                      8312.7907                     1438.9535
## 238                      8312.7907                     1438.9535
## 239                      8312.7907                     1438.9535
## 240                      8312.7907                     1438.9535
## 241                      3071.5116                        0.0000
## 242                      3071.5116                        0.0000
## 243                      3071.5116                        0.0000
## 244                      3071.5116                        0.0000
## 245                      3071.5116                        0.0000
## 246                      3071.5116                        0.0000
## 247                      3071.5116                        0.0000
## 248                      3071.5116                        0.0000
## 249                      3071.5116                        0.0000
## 250                      3071.5116                        0.0000
## 251                      3071.5116                        0.0000
## 252                      3071.5116                        0.0000
## 253                      3071.5116                        0.0000
## 254                      3071.5116                        0.0000
## 255                      3071.5116                        0.0000
## 256                      3071.5116                        0.0000
## 257                      3071.5116                        0.0000
## 258                      3071.5116                        0.0000
## 259                      3071.5116                        0.0000
## 260                      3071.5116                        0.0000
## 261                      3071.5116                        0.0000
## 262                      3071.5116                        0.0000
## 263                      3071.5116                        0.0000
## 264                      3071.5116                        0.0000
## 265                      4988.3721                        0.0000
## 266                      4988.3721                        0.0000
## 267                      4988.3721                        0.0000
## 268                      4988.3721                        0.0000
## 269                      4988.3721                        0.0000
## 270                      4988.3721                        0.0000
## 271                      4988.3721                        0.0000
## 272                      4988.3721                        0.0000
## 273                      4988.3721                        0.0000
## 274                      4988.3721                        0.0000
## 275                      4988.3721                        0.0000
## 276                      4988.3721                        0.0000
## 277                      4988.3721                        0.0000
## 278                      4988.3721                        0.0000
## 279                      4988.3721                        0.0000
## 280                      4988.3721                        0.0000
## 281                      4988.3721                        0.0000
## 282                      4988.3721                        0.0000
## 283                      4988.3721                        0.0000
## 284                      4988.3721                        0.0000
## 285                      4988.3721                        0.0000
## 286                      4988.3721                        0.0000
## 287                      4988.3721                        0.0000
## 288                      4988.3721                        0.0000
## 289                      4534.8837                      436.0465
## 290                      4534.8837                      436.0465
## 291                      4534.8837                      436.0465
## 292                      4534.8837                      436.0465
## 293                      4534.8837                      436.0465
## 294                      4534.8837                      436.0465
## 295                      4534.8837                      436.0465
## 296                      4534.8837                      436.0465
## 297                      4534.8837                      436.0465
## 298                      4534.8837                      436.0465
## 299                      4534.8837                      436.0465
## 300                      4534.8837                      436.0465
## 301                      4534.8837                      436.0465
## 302                      4534.8837                      436.0465
## 303                      4534.8837                      436.0465
## 304                      4534.8837                      436.0465
## 305                      4534.8837                      436.0465
## 306                      4534.8837                      436.0465
## 307                      4534.8837                      436.0465
## 308                      4534.8837                      436.0465
## 309                      4534.8837                      436.0465
## 310                      4534.8837                      436.0465
## 311                      4534.8837                      436.0465
## 312                      4534.8837                      436.0465
## 313                      1456.3953                        0.0000
## 314                      1456.3953                        0.0000
## 315                      1456.3953                        0.0000
## 316                      1456.3953                        0.0000
## 317                      1456.3953                        0.0000
## 318                      1456.3953                        0.0000
## 319                      1456.3953                        0.0000
## 320                      1456.3953                        0.0000
## 321                      1456.3953                        0.0000
## 322                      1456.3953                        0.0000
## 323                      1456.3953                        0.0000
## 324                      1456.3953                        0.0000
## 325                      1456.3953                        0.0000
## 326                      1456.3953                        0.0000
## 327                      1456.3953                        0.0000
## 328                      1456.3953                        0.0000
## 329                      1456.3953                        0.0000
## 330                      1456.3953                        0.0000
## 331                      1456.3953                        0.0000
## 332                      1456.3953                        0.0000
## 333                      1456.3953                        0.0000
## 334                      1456.3953                        0.0000
## 335                      1456.3953                        0.0000
## 336                      1456.3953                        0.0000
## 337                      1059.5930                        0.0000
## 338                      1059.5930                        0.0000
## 339                      1059.5930                        0.0000
## 340                      1059.5930                        0.0000
## 341                      1059.5930                        0.0000
## 342                      1059.5930                        0.0000
## 343                      1059.5930                        0.0000
## 344                      1059.5930                        0.0000
## 345                      1059.5930                        0.0000
## 346                      1059.5930                        0.0000
## 347                      1059.5930                        0.0000
## 348                      1059.5930                        0.0000
## 349                      1059.5930                        0.0000
## 350                      1059.5930                        0.0000
## 351                      1059.5930                        0.0000
## 352                      1059.5930                        0.0000
## 353                      1059.5930                        0.0000
## 354                      1059.5930                        0.0000
## 355                      1059.5930                        0.0000
## 356                      1059.5930                        0.0000
## 357                      1059.5930                        0.0000
## 358                      1059.5930                        0.0000
## 359                      1059.5930                        0.0000
## 360                      1059.5930                        0.0000
## 361                      1360.4651                      545.0581
## 362                      1360.4651                      545.0581
## 363                      1360.4651                      545.0581
## 364                      1360.4651                      545.0581
## 365                      1360.4651                      545.0581
## 366                      1360.4651                      545.0581
## 367                      1360.4651                      545.0581
## 368                      1360.4651                      545.0581
## 369                      1360.4651                      545.0581
## 370                      1360.4651                      545.0581
## 371                      1360.4651                      545.0581
## 372                      1360.4651                      545.0581
## 373                      1360.4651                      545.0581
## 374                      1360.4651                      545.0581
## 375                      1360.4651                      545.0581
## 376                      1360.4651                      545.0581
## 377                      1360.4651                      545.0581
## 378                      1360.4651                      545.0581
## 379                      1360.4651                      545.0581
## 380                      1360.4651                      545.0581
## 381                      1360.4651                      545.0581
## 382                      1360.4651                      545.0581
## 383                      1360.4651                      545.0581
## 384                      1360.4651                      545.0581
## 385                      3155.2326                     2494.1860
## 386                      3155.2326                     2494.1860
## 387                      3155.2326                     2494.1860
## 388                      3155.2326                     2494.1860
## 389                      3155.2326                     2494.1860
## 390                      3155.2326                     2494.1860
## 391                      3155.2326                     2494.1860
## 392                      3155.2326                     2494.1860
## 393                      3155.2326                     2494.1860
## 394                      3155.2326                     2494.1860
## 395                      3155.2326                     2494.1860
## 396                      3155.2326                     2494.1860
## 397                      3155.2326                     2494.1860
## 398                      3155.2326                     2494.1860
## 399                      3155.2326                     2494.1860
## 400                      3155.2326                     2494.1860
## 401                      3155.2326                     2494.1860
## 402                      3155.2326                     2494.1860
## 403                      3155.2326                     2494.1860
## 404                      3155.2326                     2494.1860
## 405                      3155.2326                     2494.1860
## 406                      3155.2326                     2494.1860
## 407                      3155.2326                     2494.1860
## 408                      3155.2326                     2494.1860
## 409                      2190.6977                     2188.9535
## 410                      2190.6977                     2188.9535
## 411                      2190.6977                     2188.9535
## 412                      2190.6977                     2188.9535
## 413                      2190.6977                     2188.9535
## 414                      2190.6977                     2188.9535
## 415                      2190.6977                     2188.9535
## 416                      2190.6977                     2188.9535
## 417                      2190.6977                     2188.9535
## 418                      2190.6977                     2188.9535
## 419                      2190.6977                     2188.9535
## 420                      2190.6977                     2188.9535
## 421                      2190.6977                     2188.9535
## 422                      2190.6977                     2188.9535
## 423                      2190.6977                     2188.9535
## 424                      2190.6977                     2188.9535
## 425                      2190.6977                     2188.9535
## 426                      2190.6977                     2188.9535
## 427                      2190.6977                     2188.9535
## 428                      2190.6977                     2188.9535
## 429                      2190.6977                     2188.9535
## 430                      2190.6977                     2188.9535
## 431                      2190.6977                     2188.9535
## 432                      2190.6977                     2188.9535
## 433                      6586.0465                      244.1860
## 434                      6586.0465                      244.1860
## 435                      6586.0465                      244.1860
## 436                      6586.0465                      244.1860
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## 1730                     3155.2326                     2494.1860
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## 1754                     6062.7907                     2283.1395
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## 1827                     3235.4651                     1090.1163
## 1828                     3235.4651                     1090.1163
## 1829                     3235.4651                     1090.1163
## 1830                     3235.4651                     1090.1163
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## 1839                     3235.4651                     1090.1163
## 1840                     3235.4651                     1090.1163
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## 1845                     3235.4651                     1090.1163
## 1846                     3235.4651                     1090.1163
## 1847                     3235.4651                     1090.1163
## 1848                     3235.4651                     1090.1163
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## 1858                     2581.3953                     1875.0000
## 1859                     2581.3953                     1875.0000
## 1860                     2581.3953                     1875.0000
## 1861                     2581.3953                     1875.0000
## 1862                     2581.3953                     1875.0000
## 1863                     2581.3953                     1875.0000
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## 1865                     2581.3953                     1875.0000
## 1866                     2581.3953                     1875.0000
## 1867                     2581.3953                     1875.0000
## 1868                     2581.3953                     1875.0000
## 1869                     2581.3953                     1875.0000
## 1870                     2581.3953                     1875.0000
## 1871                     2581.3953                     1875.0000
## 1872                     2581.3953                     1875.0000
## 1873                     1046.5116                     1521.8023
## 1874                     1046.5116                     1521.8023
## 1875                     1046.5116                     1521.8023
## 1876                     1046.5116                     1521.8023
## 1877                     1046.5116                     1521.8023
## 1878                     1046.5116                     1521.8023
## 1879                     1046.5116                     1521.8023
## 1880                     1046.5116                     1521.8023
## 1881                     1046.5116                     1521.8023
## 1882                     1046.5116                     1521.8023
## 1883                     1046.5116                     1521.8023
## 1884                     1046.5116                     1521.8023
## 1885                     1046.5116                     1521.8023
## 1886                     1046.5116                     1521.8023
## 1887                     1046.5116                     1521.8023
## 1888                     1046.5116                     1521.8023
## 1889                     1046.5116                     1521.8023
## 1890                     1046.5116                     1521.8023
## 1891                     1046.5116                     1521.8023
## 1892                     1046.5116                     1521.8023
## 1893                     1046.5116                     1521.8023
## 1894                     1046.5116                     1521.8023
## 1895                     1046.5116                     1521.8023
## 1896                     1046.5116                     1521.8023
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## 1898                     1090.1163                      545.0581
## 1899                     1090.1163                      545.0581
## 1900                     1090.1163                      545.0581
## 1901                     1090.1163                      545.0581
## 1902                     1090.1163                      545.0581
## 1903                     1090.1163                      545.0581
## 1904                     1090.1163                      545.0581
## 1905                     1090.1163                      545.0581
## 1906                     1090.1163                      545.0581
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## 1908                     1090.1163                      545.0581
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## 1913                     1090.1163                      545.0581
## 1914                     1090.1163                      545.0581
## 1915                     1090.1163                      545.0581
## 1916                     1090.1163                      545.0581
## 1917                     1090.1163                      545.0581
## 1918                     1090.1163                      545.0581
## 1919                     1090.1163                      545.0581
## 1920                     1090.1163                      545.0581
## 1921                     3155.2326                     2494.1860
## 1922                     3155.2326                     2494.1860
## 1923                     3155.2326                     2494.1860
## 1924                     3155.2326                     2494.1860
## 1925                     3155.2326                     2494.1860
## 1926                     3155.2326                     2494.1860
## 1927                     3155.2326                     2494.1860
## 1928                     3155.2326                     2494.1860
## 1929                     3155.2326                     2494.1860
## 1930                     3155.2326                     2494.1860
## 1931                     3155.2326                     2494.1860
## 1932                     3155.2326                     2494.1860
## 1933                     3155.2326                     2494.1860
## 1934                     3155.2326                     2494.1860
## 1935                     3155.2326                     2494.1860
## 1936                     3155.2326                     2494.1860
## 1937                     3155.2326                     2494.1860
## 1938                     3155.2326                     2494.1860
## 1939                     3155.2326                     2494.1860
## 1940                     3155.2326                     2494.1860
## 1941                     3155.2326                     2494.1860
## 1942                     3155.2326                     2494.1860
## 1943                     3155.2326                     2494.1860
## 1944                     3155.2326                     2494.1860
## 1945                     3579.0698                        0.0000
## 1946                     3579.0698                        0.0000
## 1947                     3579.0698                        0.0000
## 1948                     3579.0698                        0.0000
## 1949                     3579.0698                        0.0000
## 1950                     3579.0698                        0.0000
## 1951                     3579.0698                        0.0000
## 1952                     3579.0698                        0.0000
## 1953                     3579.0698                        0.0000
## 1954                     3579.0698                        0.0000
## 1955                     3579.0698                        0.0000
## 1956                     3579.0698                        0.0000
## 1957                     3579.0698                        0.0000
## 1958                     3579.0698                        0.0000
## 1959                     3579.0698                        0.0000
## 1960                     3579.0698                        0.0000
## 1961                     3579.0698                        0.0000
## 1962                     3579.0698                        0.0000
## 1963                     3579.0698                        0.0000
## 1964                     3579.0698                        0.0000
## 1965                     3579.0698                        0.0000
## 1966                     3579.0698                        0.0000
## 1967                     3579.0698                        0.0000
## 1968                     3579.0698                        0.0000
## 1969                     1381.3953                        0.0000
## 1970                     1381.3953                        0.0000
## 1971                     1381.3953                        0.0000
## 1972                     1381.3953                        0.0000
## 1973                     1381.3953                        0.0000
## 1974                     1381.3953                        0.0000
## 1975                     1381.3953                        0.0000
## 1976                     1381.3953                        0.0000
## 1977                     1381.3953                        0.0000
## 1978                     1381.3953                        0.0000
## 1979                     1381.3953                        0.0000
## 1980                     1381.3953                        0.0000
## 1981                     1381.3953                        0.0000
## 1982                     1381.3953                        0.0000
## 1983                     1381.3953                        0.0000
## 1984                     1381.3953                        0.0000
## 1985                     1381.3953                        0.0000
## 1986                     1381.3953                        0.0000
## 1987                     1381.3953                        0.0000
## 1988                     1381.3953                        0.0000
## 1989                     1381.3953                        0.0000
## 1990                     1381.3953                        0.0000
## 1991                     1381.3953                        0.0000
## 1992                     1381.3953                        0.0000
## 1993                     5084.3023                        0.0000
## 1994                     5084.3023                        0.0000
## 1995                     5084.3023                        0.0000
## 1996                     5084.3023                        0.0000
## 1997                     5084.3023                        0.0000
## 1998                     5084.3023                        0.0000
## 1999                     5084.3023                        0.0000
## 2000                     5084.3023                        0.0000
## 2001                     5084.3023                        0.0000
## 2002                     5084.3023                        0.0000
## 2003                     5084.3023                        0.0000
## 2004                     5084.3023                        0.0000
## 2005                     5084.3023                        0.0000
## 2006                     5084.3023                        0.0000
## 2007                     5084.3023                        0.0000
## 2008                     5084.3023                        0.0000
## 2009                     5084.3023                        0.0000
## 2010                     5084.3023                        0.0000
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## 3054                     2646.8023                     1630.8140
## 3055                     2646.8023                     1630.8140
## 3056                     2646.8023                     1630.8140
## 3057                     2646.8023                     1630.8140
## 3058                     2646.8023                     1630.8140
## 3059                     2646.8023                     1630.8140
## 3060                     2646.8023                     1630.8140
## 3061                     2646.8023                     1630.8140
## 3062                     2646.8023                     1630.8140
## 3063                     2646.8023                     1630.8140
## 3064                     2646.8023                     1630.8140
## 3065                     2646.8023                     1630.8140
## 3066                     2646.8023                     1630.8140
## 3067                     2646.8023                     1630.8140
## 3068                     2646.8023                     1630.8140
## 3069                     2646.8023                     1630.8140
## 3070                     2646.8023                     1630.8140
## 3071                     2646.8023                     1630.8140
## 3072                     2646.8023                     1630.8140
## 3073                     3155.2326                     2494.1860
## 3074                     3155.2326                     2494.1860
## 3075                     3155.2326                     2494.1860
## 3076                     3155.2326                     2494.1860
## 3077                     3155.2326                     2494.1860
## 3078                     3155.2326                     2494.1860
## 3079                     3155.2326                     2494.1860
## 3080                     3155.2326                     2494.1860
## 3081                     3155.2326                     2494.1860
## 3082                     3155.2326                     2494.1860
## 3083                     3155.2326                     2494.1860
## 3084                     3155.2326                     2494.1860
## 3085                     3155.2326                     2494.1860
## 3086                     3155.2326                     2494.1860
## 3087                     3155.2326                     2494.1860
## 3088                     3155.2326                     2494.1860
## 3089                     3155.2326                     2494.1860
## 3090                     3155.2326                     2494.1860
## 3091                     3155.2326                     2494.1860
## 3092                     3155.2326                     2494.1860
## 3093                     3155.2326                     2494.1860
## 3094                     3155.2326                     2494.1860
## 3095                     3155.2326                     2494.1860
## 3096                     3155.2326                     2494.1860
## 3097                     7639.5349                     1220.9302
## 3098                     7639.5349                     1220.9302
## 3099                     7639.5349                     1220.9302
## 3100                     7639.5349                     1220.9302
## 3101                     7639.5349                     1220.9302
## 3102                     7639.5349                     1220.9302
## 3103                     7639.5349                     1220.9302
## 3104                     7639.5349                     1220.9302
## 3105                     7639.5349                     1220.9302
## 3106                     7639.5349                     1220.9302
## 3107                     7639.5349                     1220.9302
## 3108                     7639.5349                     1220.9302
## 3109                     7639.5349                     1220.9302
## 3110                     7639.5349                     1220.9302
## 3111                     7639.5349                     1220.9302
## 3112                     7639.5349                     1220.9302
## 3113                     7639.5349                     1220.9302
## 3114                     7639.5349                     1220.9302
## 3115                     7639.5349                     1220.9302
## 3116                     7639.5349                     1220.9302
## 3117                     7639.5349                     1220.9302
## 3118                     7639.5349                     1220.9302
## 3119                     7639.5349                     1220.9302
## 3120                     7639.5349                     1220.9302
## 3121                     3640.1163                      218.0233
## 3122                     3640.1163                      218.0233
## 3123                     3640.1163                      218.0233
## 3124                     3640.1163                      218.0233
## 3125                     3640.1163                      218.0233
## 3126                     3640.1163                      218.0233
## 3127                     3640.1163                      218.0233
## 3128                     3640.1163                      218.0233
## 3129                     3640.1163                      218.0233
## 3130                     3640.1163                      218.0233
## 3131                     3640.1163                      218.0233
## 3132                     3640.1163                      218.0233
## 3133                     3640.1163                      218.0233
## 3134                     3640.1163                      218.0233
## 3135                     3640.1163                      218.0233
## 3136                     3640.1163                      218.0233
## 3137                     3640.1163                      218.0233
## 3138                     3640.1163                      218.0233
## 3139                     3640.1163                      218.0233
## 3140                     3640.1163                      218.0233
## 3141                     3640.1163                      218.0233
## 3142                     3640.1163                      218.0233
## 3143                     3640.1163                      218.0233
## 3144                     3640.1163                      218.0233
## 3145                     4988.3721                        0.0000
## 3146                     4988.3721                        0.0000
## 3147                     4988.3721                        0.0000
## 3148                     4988.3721                        0.0000
## 3149                     4988.3721                        0.0000
## 3150                     4988.3721                        0.0000
## 3151                     4988.3721                        0.0000
## 3152                     4988.3721                        0.0000
## 3153                     4988.3721                        0.0000
## 3154                     4988.3721                        0.0000
## 3155                     4988.3721                        0.0000
## 3156                     4988.3721                        0.0000
## 3157                     4988.3721                        0.0000
## 3158                     4988.3721                        0.0000
## 3159                     4988.3721                        0.0000
## 3160                     4988.3721                        0.0000
## 3161                     4988.3721                        0.0000
## 3162                     4988.3721                        0.0000
## 3163                     4988.3721                        0.0000
## 3164                     4988.3721                        0.0000
## 3165                     4988.3721                        0.0000
## 3166                     4988.3721                        0.0000
## 3167                     4988.3721                        0.0000
## 3168                     4988.3721                        0.0000
## 3169                     4116.2791                        0.0000
## 3170                     4116.2791                        0.0000
## 3171                     4116.2791                        0.0000
## 3172                     4116.2791                        0.0000
## 3173                     4116.2791                        0.0000
## 3174                     4116.2791                        0.0000
## 3175                     4116.2791                        0.0000
## 3176                     4116.2791                        0.0000
## 3177                     4116.2791                        0.0000
## 3178                     4116.2791                        0.0000
## 3179                     4116.2791                        0.0000
## 3180                     4116.2791                        0.0000
## 3181                     4116.2791                        0.0000
## 3182                     4116.2791                        0.0000
## 3183                     4116.2791                        0.0000
## 3184                     4116.2791                        0.0000
## 3185                     4116.2791                        0.0000
## 3186                     4116.2791                        0.0000
## 3187                     4116.2791                        0.0000
## 3188                     4116.2791                        0.0000
## 3189                     4116.2791                        0.0000
## 3190                     4116.2791                        0.0000
## 3191                     4116.2791                        0.0000
## 3192                     4116.2791                        0.0000
## 3193                     1674.4186                        0.0000
## 3194                     1674.4186                        0.0000
## 3195                     1674.4186                        0.0000
## 3196                     1674.4186                        0.0000
## 3197                     1674.4186                        0.0000
## 3198                     1674.4186                        0.0000
## 3199                     1674.4186                        0.0000
## 3200                     1674.4186                        0.0000
## 3201                     1674.4186                        0.0000
## 3202                     1674.4186                        0.0000
## 3203                     1674.4186                        0.0000
## 3204                     1674.4186                        0.0000
## 3205                     1674.4186                        0.0000
## 3206                     1674.4186                        0.0000
## 3207                     1674.4186                        0.0000
## 3208                     1674.4186                        0.0000
## 3209                     1674.4186                        0.0000
## 3210                     1674.4186                        0.0000
## 3211                     1674.4186                        0.0000
## 3212                     1674.4186                        0.0000
## 3213                     1674.4186                        0.0000
## 3214                     1674.4186                        0.0000
## 3215                     1674.4186                        0.0000
## 3216                     1674.4186                        0.0000
## 3217                     1059.5930                        0.0000
## 3218                     1059.5930                        0.0000
## 3219                     1059.5930                        0.0000
## 3220                     1059.5930                        0.0000
## 3221                     1059.5930                        0.0000
## 3222                     1059.5930                        0.0000
## 3223                     1059.5930                        0.0000
## 3224                     1059.5930                        0.0000
## 3225                     1059.5930                        0.0000
##      total_metaecosystem_Pau_indiv total_metaecosystem_Pca_indiv
## 1                        5161.0465                     883.43023
## 2                        5161.0465                     883.43023
## 3                        5161.0465                     883.43023
## 4                        5161.0465                     883.43023
## 5                        5161.0465                     883.43023
## 6                        5161.0465                     883.43023
## 7                        5161.0465                     883.43023
## 8                        5161.0465                     883.43023
## 9                        5161.0465                     883.43023
## 10                       5161.0465                     883.43023
## 11                       5161.0465                     883.43023
## 12                       5161.0465                     883.43023
## 13                       5161.0465                     883.43023
## 14                       5161.0465                     883.43023
## 15                       5161.0465                     883.43023
## 16                       5161.0465                     883.43023
## 17                       5161.0465                     883.43023
## 18                       5161.0465                     883.43023
## 19                       5161.0465                     883.43023
## 20                       5161.0465                     883.43023
## 21                       5161.0465                     883.43023
## 22                       5161.0465                     883.43023
## 23                       5161.0465                     883.43023
## 24                       5161.0465                     883.43023
## 25                          0.0000                    1854.06977
## 26                          0.0000                    1854.06977
## 27                          0.0000                    1854.06977
## 28                          0.0000                    1854.06977
## 29                          0.0000                    1854.06977
## 30                          0.0000                    1854.06977
## 31                          0.0000                    1854.06977
## 32                          0.0000                    1854.06977
## 33                          0.0000                    1854.06977
## 34                          0.0000                    1854.06977
## 35                          0.0000                    1854.06977
## 36                          0.0000                    1854.06977
## 37                          0.0000                    1854.06977
## 38                          0.0000                    1854.06977
## 39                          0.0000                    1854.06977
## 40                          0.0000                    1854.06977
## 41                          0.0000                    1854.06977
## 42                          0.0000                    1854.06977
## 43                          0.0000                    1854.06977
## 44                          0.0000                    1854.06977
## 45                          0.0000                    1854.06977
## 46                          0.0000                    1854.06977
## 47                          0.0000                    1854.06977
## 48                          0.0000                    1854.06977
## 49                       1970.9302                    1189.53488
## 50                       1970.9302                    1189.53488
## 51                       1970.9302                    1189.53488
## 52                       1970.9302                    1189.53488
## 53                       1970.9302                    1189.53488
## 54                       1970.9302                    1189.53488
## 55                       1970.9302                    1189.53488
## 56                       1970.9302                    1189.53488
## 57                       1970.9302                    1189.53488
## 58                       1970.9302                    1189.53488
## 59                       1970.9302                    1189.53488
## 60                       1970.9302                    1189.53488
## 61                       1970.9302                    1189.53488
## 62                       1970.9302                    1189.53488
## 63                       1970.9302                    1189.53488
## 64                       1970.9302                    1189.53488
## 65                       1970.9302                    1189.53488
## 66                       1970.9302                    1189.53488
## 67                       1970.9302                    1189.53488
## 68                       1970.9302                    1189.53488
## 69                       1970.9302                    1189.53488
## 70                       1970.9302                    1189.53488
## 71                       1970.9302                    1189.53488
## 72                       1970.9302                    1189.53488
## 73                       1369.1860                    3783.13953
## 74                       1369.1860                    3783.13953
## 75                       1369.1860                    3783.13953
## 76                       1369.1860                    3783.13953
## 77                       1369.1860                    3783.13953
## 78                       1369.1860                    3783.13953
## 79                       1369.1860                    3783.13953
## 80                       1369.1860                    3783.13953
## 81                       1369.1860                    3783.13953
## 82                       1369.1860                    3783.13953
## 83                       1369.1860                    3783.13953
## 84                       1369.1860                    3783.13953
## 85                       1369.1860                    3783.13953
## 86                       1369.1860                    3783.13953
## 87                       1369.1860                    3783.13953
## 88                       1369.1860                    3783.13953
## 89                       1369.1860                    3783.13953
## 90                       1369.1860                    3783.13953
## 91                       1369.1860                    3783.13953
## 92                       1369.1860                    3783.13953
## 93                       1369.1860                    3783.13953
## 94                       1369.1860                    3783.13953
## 95                       1369.1860                    3783.13953
## 96                       1369.1860                    3783.13953
## 97                       2776.7442                    1709.30233
## 98                       2776.7442                    1709.30233
## 99                       2776.7442                    1709.30233
## 100                      2776.7442                    1709.30233
## 101                      2776.7442                    1709.30233
## 102                      2776.7442                    1709.30233
## 103                      2776.7442                    1709.30233
## 104                      2776.7442                    1709.30233
## 105                      2776.7442                    1709.30233
## 106                      2776.7442                    1709.30233
## 107                      2776.7442                    1709.30233
## 108                      2776.7442                    1709.30233
## 109                      2776.7442                    1709.30233
## 110                      2776.7442                    1709.30233
## 111                      2776.7442                    1709.30233
## 112                      2776.7442                    1709.30233
## 113                      2776.7442                    1709.30233
## 114                      2776.7442                    1709.30233
## 115                      2776.7442                    1709.30233
## 116                      2776.7442                    1709.30233
## 117                      2776.7442                    1709.30233
## 118                      2776.7442                    1709.30233
## 119                      2776.7442                    1709.30233
## 120                      2776.7442                    1709.30233
## 121                       559.8837                     540.69767
## 122                       559.8837                     540.69767
## 123                       559.8837                     540.69767
## 124                       559.8837                     540.69767
## 125                       559.8837                     540.69767
## 126                       559.8837                     540.69767
## 127                       559.8837                     540.69767
## 128                       559.8837                     540.69767
## 129                       559.8837                     540.69767
## 130                       559.8837                     540.69767
## 131                       559.8837                     540.69767
## 132                       559.8837                     540.69767
## 133                       559.8837                     540.69767
## 134                       559.8837                     540.69767
## 135                       559.8837                     540.69767
## 136                       559.8837                     540.69767
## 137                       559.8837                     540.69767
## 138                       559.8837                     540.69767
## 139                       559.8837                     540.69767
## 140                       559.8837                     540.69767
## 141                       559.8837                     540.69767
## 142                       559.8837                     540.69767
## 143                       559.8837                     540.69767
## 144                       559.8837                     540.69767
## 145                       109.0116                    1181.68605
## 146                       109.0116                    1181.68605
## 147                       109.0116                    1181.68605
## 148                       109.0116                    1181.68605
## 149                       109.0116                    1181.68605
## 150                       109.0116                    1181.68605
## 151                       109.0116                    1181.68605
## 152                       109.0116                    1181.68605
## 153                       109.0116                    1181.68605
## 154                       109.0116                    1181.68605
## 155                       109.0116                    1181.68605
## 156                       109.0116                    1181.68605
## 157                       109.0116                    1181.68605
## 158                       109.0116                    1181.68605
## 159                       109.0116                    1181.68605
## 160                       109.0116                    1181.68605
## 161                       109.0116                    1181.68605
## 162                       109.0116                    1181.68605
## 163                       109.0116                    1181.68605
## 164                       109.0116                    1181.68605
## 165                       109.0116                    1181.68605
## 166                       109.0116                    1181.68605
## 167                       109.0116                    1181.68605
## 168                       109.0116                    1181.68605
## 169                       531.9767                    1063.95349
## 170                       531.9767                    1063.95349
## 171                       531.9767                    1063.95349
## 172                       531.9767                    1063.95349
## 173                       531.9767                    1063.95349
## 174                       531.9767                    1063.95349
## 175                       531.9767                    1063.95349
## 176                       531.9767                    1063.95349
## 177                       531.9767                    1063.95349
## 178                       531.9767                    1063.95349
## 179                       531.9767                    1063.95349
## 180                       531.9767                    1063.95349
## 181                       531.9767                    1063.95349
## 182                       531.9767                    1063.95349
## 183                       531.9767                    1063.95349
## 184                       531.9767                    1063.95349
## 185                       531.9767                    1063.95349
## 186                       531.9767                    1063.95349
## 187                       531.9767                    1063.95349
## 188                       531.9767                    1063.95349
## 189                       531.9767                    1063.95349
## 190                       531.9767                    1063.95349
## 191                       531.9767                    1063.95349
## 192                       531.9767                    1063.95349
## 193                      5161.0465                     883.43023
## 194                      5161.0465                     883.43023
## 195                      5161.0465                     883.43023
## 196                      5161.0465                     883.43023
## 197                      5161.0465                     883.43023
## 198                      5161.0465                     883.43023
## 199                      5161.0465                     883.43023
## 200                      5161.0465                     883.43023
## 201                      5161.0465                     883.43023
## 202                      5161.0465                     883.43023
## 203                      5161.0465                     883.43023
## 204                      5161.0465                     883.43023
## 205                      5161.0465                     883.43023
## 206                      5161.0465                     883.43023
## 207                      5161.0465                     883.43023
## 208                      5161.0465                     883.43023
## 209                      5161.0465                     883.43023
## 210                      5161.0465                     883.43023
## 211                      5161.0465                     883.43023
## 212                      5161.0465                     883.43023
## 213                      5161.0465                     883.43023
## 214                      5161.0465                     883.43023
## 215                      5161.0465                     883.43023
## 216                      5161.0465                     883.43023
## 217                      5720.9302                    5708.72093
## 218                      5720.9302                    5708.72093
## 219                      5720.9302                    5708.72093
## 220                      5720.9302                    5708.72093
## 221                      5720.9302                    5708.72093
## 222                      5720.9302                    5708.72093
## 223                      5720.9302                    5708.72093
## 224                      5720.9302                    5708.72093
## 225                      5720.9302                    5708.72093
## 226                      5720.9302                    5708.72093
## 227                      5720.9302                    5708.72093
## 228                      5720.9302                    5708.72093
## 229                      5720.9302                    5708.72093
## 230                      5720.9302                    5708.72093
## 231                      5720.9302                    5708.72093
## 232                      5720.9302                    5708.72093
## 233                      5720.9302                    5708.72093
## 234                      5720.9302                    5708.72093
## 235                      5720.9302                    5708.72093
## 236                      5720.9302                    5708.72093
## 237                      5720.9302                    5708.72093
## 238                      5720.9302                    5708.72093
## 239                      5720.9302                    5708.72093
## 240                      5720.9302                    5708.72093
## 241                       331.3953                      99.41860
## 242                       331.3953                      99.41860
## 243                       331.3953                      99.41860
## 244                       331.3953                      99.41860
## 245                       331.3953                      99.41860
## 246                       331.3953                      99.41860
## 247                       331.3953                      99.41860
## 248                       331.3953                      99.41860
## 249                       331.3953                      99.41860
## 250                       331.3953                      99.41860
## 251                       331.3953                      99.41860
## 252                       331.3953                      99.41860
## 253                       331.3953                      99.41860
## 254                       331.3953                      99.41860
## 255                       331.3953                      99.41860
## 256                       331.3953                      99.41860
## 257                       331.3953                      99.41860
## 258                       331.3953                      99.41860
## 259                       331.3953                      99.41860
## 260                       331.3953                      99.41860
## 261                       331.3953                      99.41860
## 262                       331.3953                      99.41860
## 263                       331.3953                      99.41860
## 264                       331.3953                      99.41860
## 265                      3052.3256                     146.51163
## 266                      3052.3256                     146.51163
## 267                      3052.3256                     146.51163
## 268                      3052.3256                     146.51163
## 269                      3052.3256                     146.51163
## 270                      3052.3256                     146.51163
## 271                      3052.3256                     146.51163
## 272                      3052.3256                     146.51163
## 273                      3052.3256                     146.51163
## 274                      3052.3256                     146.51163
## 275                      3052.3256                     146.51163
## 276                      3052.3256                     146.51163
## 277                      3052.3256                     146.51163
## 278                      3052.3256                     146.51163
## 279                      3052.3256                     146.51163
## 280                      3052.3256                     146.51163
## 281                      3052.3256                     146.51163
## 282                      3052.3256                     146.51163
## 283                      3052.3256                     146.51163
## 284                      3052.3256                     146.51163
## 285                      3052.3256                     146.51163
## 286                      3052.3256                     146.51163
## 287                      3052.3256                     146.51163
## 288                      3052.3256                     146.51163
## 289                      2192.4419                       0.00000
## 290                      2192.4419                       0.00000
## 291                      2192.4419                       0.00000
## 292                      2192.4419                       0.00000
## 293                      2192.4419                       0.00000
## 294                      2192.4419                       0.00000
## 295                      2192.4419                       0.00000
## 296                      2192.4419                       0.00000
## 297                      2192.4419                       0.00000
## 298                      2192.4419                       0.00000
## 299                      2192.4419                       0.00000
## 300                      2192.4419                       0.00000
## 301                      2192.4419                       0.00000
## 302                      2192.4419                       0.00000
## 303                      2192.4419                       0.00000
## 304                      2192.4419                       0.00000
## 305                      2192.4419                       0.00000
## 306                      2192.4419                       0.00000
## 307                      2192.4419                       0.00000
## 308                      2192.4419                       0.00000
## 309                      2192.4419                       0.00000
## 310                      2192.4419                       0.00000
## 311                      2192.4419                       0.00000
## 312                      2192.4419                       0.00000
## 313                      1833.1395                     976.74419
## 314                      1833.1395                     976.74419
## 315                      1833.1395                     976.74419
## 316                      1833.1395                     976.74419
## 317                      1833.1395                     976.74419
## 318                      1833.1395                     976.74419
## 319                      1833.1395                     976.74419
## 320                      1833.1395                     976.74419
## 321                      1833.1395                     976.74419
## 322                      1833.1395                     976.74419
## 323                      1833.1395                     976.74419
## 324                      1833.1395                     976.74419
## 325                      1833.1395                     976.74419
## 326                      1833.1395                     976.74419
## 327                      1833.1395                     976.74419
## 328                      1833.1395                     976.74419
## 329                      1833.1395                     976.74419
## 330                      1833.1395                     976.74419
## 331                      1833.1395                     976.74419
## 332                      1833.1395                     976.74419
## 333                      1833.1395                     976.74419
## 334                      1833.1395                     976.74419
## 335                      1833.1395                     976.74419
## 336                      1833.1395                     976.74419
## 337                      1020.3488                    1360.46512
## 338                      1020.3488                    1360.46512
## 339                      1020.3488                    1360.46512
## 340                      1020.3488                    1360.46512
## 341                      1020.3488                    1360.46512
## 342                      1020.3488                    1360.46512
## 343                      1020.3488                    1360.46512
## 344                      1020.3488                    1360.46512
## 345                      1020.3488                    1360.46512
## 346                      1020.3488                    1360.46512
## 347                      1020.3488                    1360.46512
## 348                      1020.3488                    1360.46512
## 349                      1020.3488                    1360.46512
## 350                      1020.3488                    1360.46512
## 351                      1020.3488                    1360.46512
## 352                      1020.3488                    1360.46512
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## 1978                     1854.0698                    1090.11628
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## 1980                     1854.0698                    1090.11628
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## 1992                     1854.0698                    1090.11628
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## 1994                     1852.3256                    3636.62791
## 1995                     1852.3256                    3636.62791
## 1996                     1852.3256                    3636.62791
## 1997                     1852.3256                    3636.62791
## 1998                     1852.3256                    3636.62791
## 1999                     1852.3256                    3636.62791
## 2000                     1852.3256                    3636.62791
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## 2006                     1852.3256                    3636.62791
## 2007                     1852.3256                    3636.62791
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## 2009                     1852.3256                    3636.62791
## 2010                     1852.3256                    3636.62791
## 2011                     1852.3256                    3636.62791
## 2012                     1852.3256                    3636.62791
## 2013                     1852.3256                    3636.62791
## 2014                     1852.3256                    3636.62791
## 2015                     1852.3256                    3636.62791
## 2016                     1852.3256                    3636.62791
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## 2018                     2572.6744                    1709.30233
## 2019                     2572.6744                    1709.30233
## 2020                     2572.6744                    1709.30233
## 2021                     2572.6744                    1709.30233
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## 2955                     1369.1860                    3636.62791
## 2956                     1369.1860                    3636.62791
## 2957                     1369.1860                    3636.62791
## 2958                     1369.1860                    3636.62791
## 2959                     1369.1860                    3636.62791
## 2960                     1369.1860                    3636.62791
## 2961                     1369.1860                    3636.62791
## 2962                     1369.1860                    3636.62791
## 2963                     1369.1860                    3636.62791
## 2964                     1369.1860                    3636.62791
## 2965                     1369.1860                    3636.62791
## 2966                     1369.1860                    3636.62791
## 2967                     1369.1860                    3636.62791
## 2968                     1369.1860                    3636.62791
## 2969                     1369.1860                    3636.62791
## 2970                     1369.1860                    3636.62791
## 2971                     1369.1860                    3636.62791
## 2972                     1369.1860                    3636.62791
## 2973                     1369.1860                    3636.62791
## 2974                     1369.1860                    3636.62791
## 2975                     1369.1860                    3636.62791
## 2976                     1369.1860                    3636.62791
## 2977                     2532.5581                    1709.30233
## 2978                     2532.5581                    1709.30233
## 2979                     2532.5581                    1709.30233
## 2980                     2532.5581                    1709.30233
## 2981                     2532.5581                    1709.30233
## 2982                     2532.5581                    1709.30233
## 2983                     2532.5581                    1709.30233
## 2984                     2532.5581                    1709.30233
## 2985                     2532.5581                    1709.30233
## 2986                     2532.5581                    1709.30233
## 2987                     2532.5581                    1709.30233
## 2988                     2532.5581                    1709.30233
## 2989                     2532.5581                    1709.30233
## 2990                     2532.5581                    1709.30233
## 2991                     2532.5581                    1709.30233
## 2992                     2532.5581                    1709.30233
## 2993                     2532.5581                    1709.30233
## 2994                     2532.5581                    1709.30233
## 2995                     2532.5581                    1709.30233
## 2996                     2532.5581                    1709.30233
## 2997                     2532.5581                    1709.30233
## 2998                     2532.5581                    1709.30233
## 2999                     2532.5581                    1709.30233
## 3000                     2532.5581                    1709.30233
## 3001                      392.4419                     594.76744
## 3002                      392.4419                     594.76744
## 3003                      392.4419                     594.76744
## 3004                      392.4419                     594.76744
## 3005                      392.4419                     594.76744
## 3006                      392.4419                     594.76744
## 3007                      392.4419                     594.76744
## 3008                      392.4419                     594.76744
## 3009                      392.4419                     594.76744
## 3010                      392.4419                     594.76744
## 3011                      392.4419                     594.76744
## 3012                      392.4419                     594.76744
## 3013                      392.4419                     594.76744
## 3014                      392.4419                     594.76744
## 3015                      392.4419                     594.76744
## 3016                      392.4419                     594.76744
## 3017                      392.4419                     594.76744
## 3018                      392.4419                     594.76744
## 3019                      392.4419                     594.76744
## 3020                      392.4419                     594.76744
## 3021                      392.4419                     594.76744
## 3022                      392.4419                     594.76744
## 3023                      392.4419                     594.76744
## 3024                      392.4419                     594.76744
## 3025                      213.6628                    1181.68605
## 3026                      213.6628                    1181.68605
## 3027                      213.6628                    1181.68605
## 3028                      213.6628                    1181.68605
## 3029                      213.6628                    1181.68605
## 3030                      213.6628                    1181.68605
## 3031                      213.6628                    1181.68605
## 3032                      213.6628                    1181.68605
## 3033                      213.6628                    1181.68605
## 3034                      213.6628                    1181.68605
## 3035                      213.6628                    1181.68605
## 3036                      213.6628                    1181.68605
## 3037                      213.6628                    1181.68605
## 3038                      213.6628                    1181.68605
## 3039                      213.6628                    1181.68605
## 3040                      213.6628                    1181.68605
## 3041                      213.6628                    1181.68605
## 3042                      213.6628                    1181.68605
## 3043                      213.6628                    1181.68605
## 3044                      213.6628                    1181.68605
## 3045                      213.6628                    1181.68605
## 3046                      213.6628                    1181.68605
## 3047                      213.6628                    1181.68605
## 3048                      213.6628                    1181.68605
## 3049                      504.0698                    1172.96512
## 3050                      504.0698                    1172.96512
## 3051                      504.0698                    1172.96512
## 3052                      504.0698                    1172.96512
## 3053                      504.0698                    1172.96512
## 3054                      504.0698                    1172.96512
## 3055                      504.0698                    1172.96512
## 3056                      504.0698                    1172.96512
## 3057                      504.0698                    1172.96512
## 3058                      504.0698                    1172.96512
## 3059                      504.0698                    1172.96512
## 3060                      504.0698                    1172.96512
## 3061                      504.0698                    1172.96512
## 3062                      504.0698                    1172.96512
## 3063                      504.0698                    1172.96512
## 3064                      504.0698                    1172.96512
## 3065                      504.0698                    1172.96512
## 3066                      504.0698                    1172.96512
## 3067                      504.0698                    1172.96512
## 3068                      504.0698                    1172.96512
## 3069                      504.0698                    1172.96512
## 3070                      504.0698                    1172.96512
## 3071                      504.0698                    1172.96512
## 3072                      504.0698                    1172.96512
## 3073                     5161.0465                     883.43023
## 3074                     5161.0465                     883.43023
## 3075                     5161.0465                     883.43023
## 3076                     5161.0465                     883.43023
## 3077                     5161.0465                     883.43023
## 3078                     5161.0465                     883.43023
## 3079                     5161.0465                     883.43023
## 3080                     5161.0465                     883.43023
## 3081                     5161.0465                     883.43023
## 3082                     5161.0465                     883.43023
## 3083                     5161.0465                     883.43023
## 3084                     5161.0465                     883.43023
## 3085                     5161.0465                     883.43023
## 3086                     5161.0465                     883.43023
## 3087                     5161.0465                     883.43023
## 3088                     5161.0465                     883.43023
## 3089                     5161.0465                     883.43023
## 3090                     5161.0465                     883.43023
## 3091                     5161.0465                     883.43023
## 3092                     5161.0465                     883.43023
## 3093                     5161.0465                     883.43023
## 3094                     5161.0465                     883.43023
## 3095                     5161.0465                     883.43023
## 3096                     5161.0465                     883.43023
## 3097                     5823.8372                    6005.23256
## 3098                     5823.8372                    6005.23256
## 3099                     5823.8372                    6005.23256
## 3100                     5823.8372                    6005.23256
## 3101                     5823.8372                    6005.23256
## 3102                     5823.8372                    6005.23256
## 3103                     5823.8372                    6005.23256
## 3104                     5823.8372                    6005.23256
## 3105                     5823.8372                    6005.23256
## 3106                     5823.8372                    6005.23256
## 3107                     5823.8372                    6005.23256
## 3108                     5823.8372                    6005.23256
## 3109                     5823.8372                    6005.23256
## 3110                     5823.8372                    6005.23256
## 3111                     5823.8372                    6005.23256
## 3112                     5823.8372                    6005.23256
## 3113                     5823.8372                    6005.23256
## 3114                     5823.8372                    6005.23256
## 3115                     5823.8372                    6005.23256
## 3116                     5823.8372                    6005.23256
## 3117                     5823.8372                    6005.23256
## 3118                     5823.8372                    6005.23256
## 3119                     5823.8372                    6005.23256
## 3120                     5823.8372                    6005.23256
## 3121                      198.8372                       0.00000
## 3122                      198.8372                       0.00000
## 3123                      198.8372                       0.00000
## 3124                      198.8372                       0.00000
## 3125                      198.8372                       0.00000
## 3126                      198.8372                       0.00000
## 3127                      198.8372                       0.00000
## 3128                      198.8372                       0.00000
## 3129                      198.8372                       0.00000
## 3130                      198.8372                       0.00000
## 3131                      198.8372                       0.00000
## 3132                      198.8372                       0.00000
## 3133                      198.8372                       0.00000
## 3134                      198.8372                       0.00000
## 3135                      198.8372                       0.00000
## 3136                      198.8372                       0.00000
## 3137                      198.8372                       0.00000
## 3138                      198.8372                       0.00000
## 3139                      198.8372                       0.00000
## 3140                      198.8372                       0.00000
## 3141                      198.8372                       0.00000
## 3142                      198.8372                       0.00000
## 3143                      198.8372                       0.00000
## 3144                      198.8372                       0.00000
## 3145                     3052.3256                       0.00000
## 3146                     3052.3256                       0.00000
## 3147                     3052.3256                       0.00000
## 3148                     3052.3256                       0.00000
## 3149                     3052.3256                       0.00000
## 3150                     3052.3256                       0.00000
## 3151                     3052.3256                       0.00000
## 3152                     3052.3256                       0.00000
## 3153                     3052.3256                       0.00000
## 3154                     3052.3256                       0.00000
## 3155                     3052.3256                       0.00000
## 3156                     3052.3256                       0.00000
## 3157                     3052.3256                       0.00000
## 3158                     3052.3256                       0.00000
## 3159                     3052.3256                       0.00000
## 3160                     3052.3256                       0.00000
## 3161                     3052.3256                       0.00000
## 3162                     3052.3256                       0.00000
## 3163                     3052.3256                       0.00000
## 3164                     3052.3256                       0.00000
## 3165                     3052.3256                       0.00000
## 3166                     3052.3256                       0.00000
## 3167                     3052.3256                       0.00000
## 3168                     3052.3256                       0.00000
## 3169                     1948.2558                       0.00000
## 3170                     1948.2558                       0.00000
## 3171                     1948.2558                       0.00000
## 3172                     1948.2558                       0.00000
## 3173                     1948.2558                       0.00000
## 3174                     1948.2558                       0.00000
## 3175                     1948.2558                       0.00000
## 3176                     1948.2558                       0.00000
## 3177                     1948.2558                       0.00000
## 3178                     1948.2558                       0.00000
## 3179                     1948.2558                       0.00000
## 3180                     1948.2558                       0.00000
## 3181                     1948.2558                       0.00000
## 3182                     1948.2558                       0.00000
## 3183                     1948.2558                       0.00000
## 3184                     1948.2558                       0.00000
## 3185                     1948.2558                       0.00000
## 3186                     1948.2558                       0.00000
## 3187                     1948.2558                       0.00000
## 3188                     1948.2558                       0.00000
## 3189                     1948.2558                       0.00000
## 3190                     1948.2558                       0.00000
## 3191                     1948.2558                       0.00000
## 3192                     1948.2558                       0.00000
## 3193                     1665.6977                    1030.81395
## 3194                     1665.6977                    1030.81395
## 3195                     1665.6977                    1030.81395
## 3196                     1665.6977                    1030.81395
## 3197                     1665.6977                    1030.81395
## 3198                     1665.6977                    1030.81395
## 3199                     1665.6977                    1030.81395
## 3200                     1665.6977                    1030.81395
## 3201                     1665.6977                    1030.81395
## 3202                     1665.6977                    1030.81395
## 3203                     1665.6977                    1030.81395
## 3204                     1665.6977                    1030.81395
## 3205                     1665.6977                    1030.81395
## 3206                     1665.6977                    1030.81395
## 3207                     1665.6977                    1030.81395
## 3208                     1665.6977                    1030.81395
## 3209                     1665.6977                    1030.81395
## 3210                     1665.6977                    1030.81395
## 3211                     1665.6977                    1030.81395
## 3212                     1665.6977                    1030.81395
## 3213                     1665.6977                    1030.81395
## 3214                     1665.6977                    1030.81395
## 3215                     1665.6977                    1030.81395
## 3216                     1665.6977                    1030.81395
## 3217                     1125.0000                    1360.46512
## 3218                     1125.0000                    1360.46512
## 3219                     1125.0000                    1360.46512
## 3220                     1125.0000                    1360.46512
## 3221                     1125.0000                    1360.46512
## 3222                     1125.0000                    1360.46512
## 3223                     1125.0000                    1360.46512
## 3224                     1125.0000                    1360.46512
## 3225                     1125.0000                    1360.46512
##      total_metaecosystem_Spi_indiv total_metaecosystem_Spi_te_indiv
## 1                        635.75581                         981.9767
## 2                        635.75581                         981.9767
## 3                        635.75581                         981.9767
## 4                        635.75581                         981.9767
## 5                        635.75581                         981.9767
## 6                        635.75581                         981.9767
## 7                        635.75581                         981.9767
## 8                        635.75581                         981.9767
## 9                        635.75581                         981.9767
## 10                       635.75581                         981.9767
## 11                       635.75581                         981.9767
## 12                       635.75581                         981.9767
## 13                       635.75581                         981.9767
## 14                       635.75581                         981.9767
## 15                       635.75581                         981.9767
## 16                       635.75581                         981.9767
## 17                       635.75581                         981.9767
## 18                       635.75581                         981.9767
## 19                       635.75581                         981.9767
## 20                       635.75581                         981.9767
## 21                       635.75581                         981.9767
## 22                       635.75581                         981.9767
## 23                       635.75581                         981.9767
## 24                       635.75581                         981.9767
## 25                      1055.23256                        1090.1163
## 26                      1055.23256                        1090.1163
## 27                      1055.23256                        1090.1163
## 28                      1055.23256                        1090.1163
## 29                      1055.23256                        1090.1163
## 30                      1055.23256                        1090.1163
## 31                      1055.23256                        1090.1163
## 32                      1055.23256                        1090.1163
## 33                      1055.23256                        1090.1163
## 34                      1055.23256                        1090.1163
## 35                      1055.23256                        1090.1163
## 36                      1055.23256                        1090.1163
## 37                      1055.23256                        1090.1163
## 38                      1055.23256                        1090.1163
## 39                      1055.23256                        1090.1163
## 40                      1055.23256                        1090.1163
## 41                      1055.23256                        1090.1163
## 42                      1055.23256                        1090.1163
## 43                      1055.23256                        1090.1163
## 44                      1055.23256                        1090.1163
## 45                      1055.23256                        1090.1163
## 46                      1055.23256                        1090.1163
## 47                      1055.23256                        1090.1163
## 48                      1055.23256                        1090.1163
## 49                      1090.11628                        2084.3023
## 50                      1090.11628                        2084.3023
## 51                      1090.11628                        2084.3023
## 52                      1090.11628                        2084.3023
## 53                      1090.11628                        2084.3023
## 54                      1090.11628                        2084.3023
## 55                      1090.11628                        2084.3023
## 56                      1090.11628                        2084.3023
## 57                      1090.11628                        2084.3023
## 58                      1090.11628                        2084.3023
## 59                      1090.11628                        2084.3023
## 60                      1090.11628                        2084.3023
## 61                      1090.11628                        2084.3023
## 62                      1090.11628                        2084.3023
## 63                      1090.11628                        2084.3023
## 64                      1090.11628                        2084.3023
## 65                      1090.11628                        2084.3023
## 66                      1090.11628                        2084.3023
## 67                      1090.11628                        2084.3023
## 68                      1090.11628                        2084.3023
## 69                      1090.11628                        2084.3023
## 70                      1090.11628                        2084.3023
## 71                      1090.11628                        2084.3023
## 72                      1090.11628                        2084.3023
## 73                      2180.23256                        2947.6744
## 74                      2180.23256                        2947.6744
## 75                      2180.23256                        2947.6744
## 76                      2180.23256                        2947.6744
## 77                      2180.23256                        2947.6744
## 78                      2180.23256                        2947.6744
## 79                      2180.23256                        2947.6744
## 80                      2180.23256                        2947.6744
## 81                      2180.23256                        2947.6744
## 82                      2180.23256                        2947.6744
## 83                      2180.23256                        2947.6744
## 84                      2180.23256                        2947.6744
## 85                      2180.23256                        2947.6744
## 86                      2180.23256                        2947.6744
## 87                      2180.23256                        2947.6744
## 88                      2180.23256                        2947.6744
## 89                      2180.23256                        2947.6744
## 90                      2180.23256                        2947.6744
## 91                      2180.23256                        2947.6744
## 92                      2180.23256                        2947.6744
## 93                      2180.23256                        2947.6744
## 94                      2180.23256                        2947.6744
## 95                      2180.23256                        2947.6744
## 96                      2180.23256                        2947.6744
## 97                       549.41860                        1308.1395
## 98                       549.41860                        1308.1395
## 99                       549.41860                        1308.1395
## 100                      549.41860                        1308.1395
## 101                      549.41860                        1308.1395
## 102                      549.41860                        1308.1395
## 103                      549.41860                        1308.1395
## 104                      549.41860                        1308.1395
## 105                      549.41860                        1308.1395
## 106                      549.41860                        1308.1395
## 107                      549.41860                        1308.1395
## 108                      549.41860                        1308.1395
## 109                      549.41860                        1308.1395
## 110                      549.41860                        1308.1395
## 111                      549.41860                        1308.1395
## 112                      549.41860                        1308.1395
## 113                      549.41860                        1308.1395
## 114                      549.41860                        1308.1395
## 115                      549.41860                        1308.1395
## 116                      549.41860                        1308.1395
## 117                      549.41860                        1308.1395
## 118                      549.41860                        1308.1395
## 119                      549.41860                        1308.1395
## 120                      549.41860                        1308.1395
## 121                        0.00000                         767.4419
## 122                        0.00000                         767.4419
## 123                        0.00000                         767.4419
## 124                        0.00000                         767.4419
## 125                        0.00000                         767.4419
## 126                        0.00000                         767.4419
## 127                        0.00000                         767.4419
## 128                        0.00000                         767.4419
## 129                        0.00000                         767.4419
## 130                        0.00000                         767.4419
## 131                        0.00000                         767.4419
## 132                        0.00000                         767.4419
## 133                        0.00000                         767.4419
## 134                        0.00000                         767.4419
## 135                        0.00000                         767.4419
## 136                        0.00000                         767.4419
## 137                        0.00000                         767.4419
## 138                        0.00000                         767.4419
## 139                        0.00000                         767.4419
## 140                        0.00000                         767.4419
## 141                        0.00000                         767.4419
## 142                        0.00000                         767.4419
## 143                        0.00000                         767.4419
## 144                        0.00000                         767.4419
## 145                       31.39535                        1460.7558
## 146                       31.39535                        1460.7558
## 147                       31.39535                        1460.7558
## 148                       31.39535                        1460.7558
## 149                       31.39535                        1460.7558
## 150                       31.39535                        1460.7558
## 151                       31.39535                        1460.7558
## 152                       31.39535                        1460.7558
## 153                       31.39535                        1460.7558
## 154                       31.39535                        1460.7558
## 155                       31.39535                        1460.7558
## 156                       31.39535                        1460.7558
## 157                       31.39535                        1460.7558
## 158                       31.39535                        1460.7558
## 159                       31.39535                        1460.7558
## 160                       31.39535                        1460.7558
## 161                       31.39535                        1460.7558
## 162                       31.39535                        1460.7558
## 163                       31.39535                        1460.7558
## 164                       31.39535                        1460.7558
## 165                       31.39535                        1460.7558
## 166                       31.39535                        1460.7558
## 167                       31.39535                        1460.7558
## 168                       31.39535                        1460.7558
## 169                      126.45349                         187.5000
## 170                      126.45349                         187.5000
## 171                      126.45349                         187.5000
## 172                      126.45349                         187.5000
## 173                      126.45349                         187.5000
## 174                      126.45349                         187.5000
## 175                      126.45349                         187.5000
## 176                      126.45349                         187.5000
## 177                      126.45349                         187.5000
## 178                      126.45349                         187.5000
## 179                      126.45349                         187.5000
## 180                      126.45349                         187.5000
## 181                      126.45349                         187.5000
## 182                      126.45349                         187.5000
## 183                      126.45349                         187.5000
## 184                      126.45349                         187.5000
## 185                      126.45349                         187.5000
## 186                      126.45349                         187.5000
## 187                      126.45349                         187.5000
## 188                      126.45349                         187.5000
## 189                      126.45349                         187.5000
## 190                      126.45349                         187.5000
## 191                      126.45349                         187.5000
## 192                      126.45349                         187.5000
## 193                      635.75581                         981.9767
## 194                      635.75581                         981.9767
## 195                      635.75581                         981.9767
## 196                      635.75581                         981.9767
## 197                      635.75581                         981.9767
## 198                      635.75581                         981.9767
## 199                      635.75581                         981.9767
## 200                      635.75581                         981.9767
## 201                      635.75581                         981.9767
## 202                      635.75581                         981.9767
## 203                      635.75581                         981.9767
## 204                      635.75581                         981.9767
## 205                      635.75581                         981.9767
## 206                      635.75581                         981.9767
## 207                      635.75581                         981.9767
## 208                      635.75581                         981.9767
## 209                      635.75581                         981.9767
## 210                      635.75581                         981.9767
## 211                      635.75581                         981.9767
## 212                      635.75581                         981.9767
## 213                      635.75581                         981.9767
## 214                      635.75581                         981.9767
## 215                      635.75581                         981.9767
## 216                      635.75581                         981.9767
## 217                     1029.06977                           0.0000
## 218                     1029.06977                           0.0000
## 219                     1029.06977                           0.0000
## 220                     1029.06977                           0.0000
## 221                     1029.06977                           0.0000
## 222                     1029.06977                           0.0000
## 223                     1029.06977                           0.0000
## 224                     1029.06977                           0.0000
## 225                     1029.06977                           0.0000
## 226                     1029.06977                           0.0000
## 227                     1029.06977                           0.0000
## 228                     1029.06977                           0.0000
## 229                     1029.06977                           0.0000
## 230                     1029.06977                           0.0000
## 231                     1029.06977                           0.0000
## 232                     1029.06977                           0.0000
## 233                     1029.06977                           0.0000
## 234                     1029.06977                           0.0000
## 235                     1029.06977                           0.0000
## 236                     1029.06977                           0.0000
## 237                     1029.06977                           0.0000
## 238                     1029.06977                           0.0000
## 239                     1029.06977                           0.0000
## 240                     1029.06977                           0.0000
## 241                        0.00000                        1997.0930
## 242                        0.00000                        1997.0930
## 243                        0.00000                        1997.0930
## 244                        0.00000                        1997.0930
## 245                        0.00000                        1997.0930
## 246                        0.00000                        1997.0930
## 247                        0.00000                        1997.0930
## 248                        0.00000                        1997.0930
## 249                        0.00000                        1997.0930
## 250                        0.00000                        1997.0930
## 251                        0.00000                        1997.0930
## 252                        0.00000                        1997.0930
## 253                        0.00000                        1997.0930
## 254                        0.00000                        1997.0930
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## 1944                     635.75581                         981.9767
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## 1979                    1090.11628                        1793.0233
## 1980                    1090.11628                        1793.0233
## 1981                    1090.11628                        1793.0233
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## 1985                    1090.11628                        1793.0233
## 1986                    1090.11628                        1793.0233
## 1987                    1090.11628                        1793.0233
## 1988                    1090.11628                        1793.0233
## 1989                    1090.11628                        1793.0233
## 1990                    1090.11628                        1793.0233
## 1991                    1090.11628                        1793.0233
## 1992                    1090.11628                        1793.0233
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## 1994                    2180.23256                        3165.6977
## 1995                    2180.23256                        3165.6977
## 1996                    2180.23256                        3165.6977
## 1997                    2180.23256                        3165.6977
## 1998                    2180.23256                        3165.6977
## 1999                    2180.23256                        3165.6977
## 2000                    2180.23256                        3165.6977
## 2001                    2180.23256                        3165.6977
## 2002                    2180.23256                        3165.6977
## 2003                    2180.23256                        3165.6977
## 2004                    2180.23256                        3165.6977
## 2005                    2180.23256                        3165.6977
## 2006                    2180.23256                        3165.6977
## 2007                    2180.23256                        3165.6977
## 2008                    2180.23256                        3165.6977
## 2009                    2180.23256                        3165.6977
## 2010                    2180.23256                        3165.6977
## 2011                    2180.23256                        3165.6977
## 2012                    2180.23256                        3165.6977
## 2013                    2180.23256                        3165.6977
## 2014                    2180.23256                        3165.6977
## 2015                    2180.23256                        3165.6977
## 2016                    2180.23256                        3165.6977
## 2017                     549.41860                        1090.1163
## 2018                     549.41860                        1090.1163
## 2019                     549.41860                        1090.1163
## 2020                     549.41860                        1090.1163
## 2021                     549.41860                        1090.1163
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## 2330                    2162.79070                        3261.6279
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## 2878                       0.00000                        1077.0349
## 2879                       0.00000                        1077.0349
## 2880                       0.00000                        1077.0349
## 2881                     635.75581                         981.9767
## 2882                     635.75581                         981.9767
## 2883                     635.75581                         981.9767
## 2884                     635.75581                         981.9767
## 2885                     635.75581                         981.9767
## 2886                     635.75581                         981.9767
## 2887                     635.75581                         981.9767
## 2888                     635.75581                         981.9767
## 2889                     635.75581                         981.9767
## 2890                     635.75581                         981.9767
## 2891                     635.75581                         981.9767
## 2892                     635.75581                         981.9767
## 2893                     635.75581                         981.9767
## 2894                     635.75581                         981.9767
## 2895                     635.75581                         981.9767
## 2896                     635.75581                         981.9767
## 2897                     635.75581                         981.9767
## 2898                     635.75581                         981.9767
## 2899                     635.75581                         981.9767
## 2900                     635.75581                         981.9767
## 2901                     635.75581                         981.9767
## 2902                     635.75581                         981.9767
## 2903                     635.75581                         981.9767
## 2904                     635.75581                         981.9767
## 2905                    1055.23256                        1508.7209
## 2906                    1055.23256                        1508.7209
## 2907                    1055.23256                        1508.7209
## 2908                    1055.23256                        1508.7209
## 2909                    1055.23256                        1508.7209
## 2910                    1055.23256                        1508.7209
## 2911                    1055.23256                        1508.7209
## 2912                    1055.23256                        1508.7209
## 2913                    1055.23256                        1508.7209
## 2914                    1055.23256                        1508.7209
## 2915                    1055.23256                        1508.7209
## 2916                    1055.23256                        1508.7209
## 2917                    1055.23256                        1508.7209
## 2918                    1055.23256                        1508.7209
## 2919                    1055.23256                        1508.7209
## 2920                    1055.23256                        1508.7209
## 2921                    1055.23256                        1508.7209
## 2922                    1055.23256                        1508.7209
## 2923                    1055.23256                        1508.7209
## 2924                    1055.23256                        1508.7209
## 2925                    1055.23256                        1508.7209
## 2926                    1055.23256                        1508.7209
## 2927                    1055.23256                        1508.7209
## 2928                    1055.23256                        1508.7209
## 2929                    1090.11628                        1308.1395
## 2930                    1090.11628                        1308.1395
## 2931                    1090.11628                        1308.1395
## 2932                    1090.11628                        1308.1395
## 2933                    1090.11628                        1308.1395
## 2934                    1090.11628                        1308.1395
## 2935                    1090.11628                        1308.1395
## 2936                    1090.11628                        1308.1395
## 2937                    1090.11628                        1308.1395
## 2938                    1090.11628                        1308.1395
## 2939                    1090.11628                        1308.1395
## 2940                    1090.11628                        1308.1395
## 2941                    1090.11628                        1308.1395
## 2942                    1090.11628                        1308.1395
## 2943                    1090.11628                        1308.1395
## 2944                    1090.11628                        1308.1395
## 2945                    1090.11628                        1308.1395
## 2946                    1090.11628                        1308.1395
## 2947                    1090.11628                        1308.1395
## 2948                    1090.11628                        1308.1395
## 2949                    1090.11628                        1308.1395
## 2950                    1090.11628                        1308.1395
## 2951                    1090.11628                        1308.1395
## 2952                    1090.11628                        1308.1395
## 2953                    2180.23256                        2947.6744
## 2954                    2180.23256                        2947.6744
## 2955                    2180.23256                        2947.6744
## 2956                    2180.23256                        2947.6744
## 2957                    2180.23256                        2947.6744
## 2958                    2180.23256                        2947.6744
## 2959                    2180.23256                        2947.6744
## 2960                    2180.23256                        2947.6744
## 2961                    2180.23256                        2947.6744
## 2962                    2180.23256                        2947.6744
## 2963                    2180.23256                        2947.6744
## 2964                    2180.23256                        2947.6744
## 2965                    2180.23256                        2947.6744
## 2966                    2180.23256                        2947.6744
## 2967                    2180.23256                        2947.6744
## 2968                    2180.23256                        2947.6744
## 2969                    2180.23256                        2947.6744
## 2970                    2180.23256                        2947.6744
## 2971                    2180.23256                        2947.6744
## 2972                    2180.23256                        2947.6744
## 2973                    2180.23256                        2947.6744
## 2974                    2180.23256                        2947.6744
## 2975                    2180.23256                        2947.6744
## 2976                    2180.23256                        2947.6744
## 2977                     549.41860                        1090.1163
## 2978                     549.41860                        1090.1163
## 2979                     549.41860                        1090.1163
## 2980                     549.41860                        1090.1163
## 2981                     549.41860                        1090.1163
## 2982                     549.41860                        1090.1163
## 2983                     549.41860                        1090.1163
## 2984                     549.41860                        1090.1163
## 2985                     549.41860                        1090.1163
## 2986                     549.41860                        1090.1163
## 2987                     549.41860                        1090.1163
## 2988                     549.41860                        1090.1163
## 2989                     549.41860                        1090.1163
## 2990                     549.41860                        1090.1163
## 2991                     549.41860                        1090.1163
## 2992                     549.41860                        1090.1163
## 2993                     549.41860                        1090.1163
## 2994                     549.41860                        1090.1163
## 2995                     549.41860                        1090.1163
## 2996                     549.41860                        1090.1163
## 2997                     549.41860                        1090.1163
## 2998                     549.41860                        1090.1163
## 2999                     549.41860                        1090.1163
## 3000                     549.41860                        1090.1163
## 3001                       0.00000                         767.4419
## 3002                       0.00000                         767.4419
## 3003                       0.00000                         767.4419
## 3004                       0.00000                         767.4419
## 3005                       0.00000                         767.4419
## 3006                       0.00000                         767.4419
## 3007                       0.00000                         767.4419
## 3008                       0.00000                         767.4419
## 3009                       0.00000                         767.4419
## 3010                       0.00000                         767.4419
## 3011                       0.00000                         767.4419
## 3012                       0.00000                         767.4419
## 3013                       0.00000                         767.4419
## 3014                       0.00000                         767.4419
## 3015                       0.00000                         767.4419
## 3016                       0.00000                         767.4419
## 3017                       0.00000                         767.4419
## 3018                       0.00000                         767.4419
## 3019                       0.00000                         767.4419
## 3020                       0.00000                         767.4419
## 3021                       0.00000                         767.4419
## 3022                       0.00000                         767.4419
## 3023                       0.00000                         767.4419
## 3024                       0.00000                         767.4419
## 3025                       0.00000                        1351.7442
## 3026                       0.00000                        1351.7442
## 3027                       0.00000                        1351.7442
## 3028                       0.00000                        1351.7442
## 3029                       0.00000                        1351.7442
## 3030                       0.00000                        1351.7442
## 3031                       0.00000                        1351.7442
## 3032                       0.00000                        1351.7442
## 3033                       0.00000                        1351.7442
## 3034                       0.00000                        1351.7442
## 3035                       0.00000                        1351.7442
## 3036                       0.00000                        1351.7442
## 3037                       0.00000                        1351.7442
## 3038                       0.00000                        1351.7442
## 3039                       0.00000                        1351.7442
## 3040                       0.00000                        1351.7442
## 3041                       0.00000                        1351.7442
## 3042                       0.00000                        1351.7442
## 3043                       0.00000                        1351.7442
## 3044                       0.00000                        1351.7442
## 3045                       0.00000                        1351.7442
## 3046                       0.00000                        1351.7442
## 3047                       0.00000                        1351.7442
## 3048                       0.00000                        1351.7442
## 3049                     126.45349                         187.5000
## 3050                     126.45349                         187.5000
## 3051                     126.45349                         187.5000
## 3052                     126.45349                         187.5000
## 3053                     126.45349                         187.5000
## 3054                     126.45349                         187.5000
## 3055                     126.45349                         187.5000
## 3056                     126.45349                         187.5000
## 3057                     126.45349                         187.5000
## 3058                     126.45349                         187.5000
## 3059                     126.45349                         187.5000
## 3060                     126.45349                         187.5000
## 3061                     126.45349                         187.5000
## 3062                     126.45349                         187.5000
## 3063                     126.45349                         187.5000
## 3064                     126.45349                         187.5000
## 3065                     126.45349                         187.5000
## 3066                     126.45349                         187.5000
## 3067                     126.45349                         187.5000
## 3068                     126.45349                         187.5000
## 3069                     126.45349                         187.5000
## 3070                     126.45349                         187.5000
## 3071                     126.45349                         187.5000
## 3072                     126.45349                         187.5000
## 3073                     635.75581                         981.9767
## 3074                     635.75581                         981.9767
## 3075                     635.75581                         981.9767
## 3076                     635.75581                         981.9767
## 3077                     635.75581                         981.9767
## 3078                     635.75581                         981.9767
## 3079                     635.75581                         981.9767
## 3080                     635.75581                         981.9767
## 3081                     635.75581                         981.9767
## 3082                     635.75581                         981.9767
## 3083                     635.75581                         981.9767
## 3084                     635.75581                         981.9767
## 3085                     635.75581                         981.9767
## 3086                     635.75581                         981.9767
## 3087                     635.75581                         981.9767
## 3088                     635.75581                         981.9767
## 3089                     635.75581                         981.9767
## 3090                     635.75581                         981.9767
## 3091                     635.75581                         981.9767
## 3092                     635.75581                         981.9767
## 3093                     635.75581                         981.9767
## 3094                     635.75581                         981.9767
## 3095                     635.75581                         981.9767
## 3096                     635.75581                         981.9767
## 3097                    1029.06977                         418.6047
## 3098                    1029.06977                         418.6047
## 3099                    1029.06977                         418.6047
## 3100                    1029.06977                         418.6047
## 3101                    1029.06977                         418.6047
## 3102                    1029.06977                         418.6047
## 3103                    1029.06977                         418.6047
## 3104                    1029.06977                         418.6047
## 3105                    1029.06977                         418.6047
## 3106                    1029.06977                         418.6047
## 3107                    1029.06977                         418.6047
## 3108                    1029.06977                         418.6047
## 3109                    1029.06977                         418.6047
## 3110                    1029.06977                         418.6047
## 3111                    1029.06977                         418.6047
## 3112                    1029.06977                         418.6047
## 3113                    1029.06977                         418.6047
## 3114                    1029.06977                         418.6047
## 3115                    1029.06977                         418.6047
## 3116                    1029.06977                         418.6047
## 3117                    1029.06977                         418.6047
## 3118                    1029.06977                         418.6047
## 3119                    1029.06977                         418.6047
## 3120                    1029.06977                         418.6047
## 3121                       0.00000                        1220.9302
## 3122                       0.00000                        1220.9302
## 3123                       0.00000                        1220.9302
## 3124                       0.00000                        1220.9302
## 3125                       0.00000                        1220.9302
## 3126                       0.00000                        1220.9302
## 3127                       0.00000                        1220.9302
## 3128                       0.00000                        1220.9302
## 3129                       0.00000                        1220.9302
## 3130                       0.00000                        1220.9302
## 3131                       0.00000                        1220.9302
## 3132                       0.00000                        1220.9302
## 3133                       0.00000                        1220.9302
## 3134                       0.00000                        1220.9302
## 3135                       0.00000                        1220.9302
## 3136                       0.00000                        1220.9302
## 3137                       0.00000                        1220.9302
## 3138                       0.00000                        1220.9302
## 3139                       0.00000                        1220.9302
## 3140                       0.00000                        1220.9302
## 3141                       0.00000                        1220.9302
## 3142                       0.00000                        1220.9302
## 3143                       0.00000                        1220.9302
## 3144                       0.00000                        1220.9302
## 3145                    2188.95349                        3122.0930
## 3146                    2188.95349                        3122.0930
## 3147                    2188.95349                        3122.0930
## 3148                    2188.95349                        3122.0930
## 3149                    2188.95349                        3122.0930
## 3150                    2188.95349                        3122.0930
## 3151                    2188.95349                        3122.0930
## 3152                    2188.95349                        3122.0930
## 3153                    2188.95349                        3122.0930
## 3154                    2188.95349                        3122.0930
## 3155                    2188.95349                        3122.0930
## 3156                    2188.95349                        3122.0930
## 3157                    2188.95349                        3122.0930
## 3158                    2188.95349                        3122.0930
## 3159                    2188.95349                        3122.0930
## 3160                    2188.95349                        3122.0930
## 3161                    2188.95349                        3122.0930
## 3162                    2188.95349                        3122.0930
## 3163                    2188.95349                        3122.0930
## 3164                    2188.95349                        3122.0930
## 3165                    2188.95349                        3122.0930
## 3166                    2188.95349                        3122.0930
## 3167                    2188.95349                        3122.0930
## 3168                    2188.95349                        3122.0930
## 3169                    3654.06977                           0.0000
## 3170                    3654.06977                           0.0000
## 3171                    3654.06977                           0.0000
## 3172                    3654.06977                           0.0000
## 3173                    3654.06977                           0.0000
## 3174                    3654.06977                           0.0000
## 3175                    3654.06977                           0.0000
## 3176                    3654.06977                           0.0000
## 3177                    3654.06977                           0.0000
## 3178                    3654.06977                           0.0000
## 3179                    3654.06977                           0.0000
## 3180                    3654.06977                           0.0000
## 3181                    3654.06977                           0.0000
## 3182                    3654.06977                           0.0000
## 3183                    3654.06977                           0.0000
## 3184                    3654.06977                           0.0000
## 3185                    3654.06977                           0.0000
## 3186                    3654.06977                           0.0000
## 3187                    3654.06977                           0.0000
## 3188                    3654.06977                           0.0000
## 3189                    3654.06977                           0.0000
## 3190                    3654.06977                           0.0000
## 3191                    3654.06977                           0.0000
## 3192                    3654.06977                           0.0000
## 3193                     287.79070                        3270.3488
## 3194                     287.79070                        3270.3488
## 3195                     287.79070                        3270.3488
## 3196                     287.79070                        3270.3488
## 3197                     287.79070                        3270.3488
## 3198                     287.79070                        3270.3488
## 3199                     287.79070                        3270.3488
## 3200                     287.79070                        3270.3488
## 3201                     287.79070                        3270.3488
## 3202                     287.79070                        3270.3488
## 3203                     287.79070                        3270.3488
## 3204                     287.79070                        3270.3488
## 3205                     287.79070                        3270.3488
## 3206                     287.79070                        3270.3488
## 3207                     287.79070                        3270.3488
## 3208                     287.79070                        3270.3488
## 3209                     287.79070                        3270.3488
## 3210                     287.79070                        3270.3488
## 3211                     287.79070                        3270.3488
## 3212                     287.79070                        3270.3488
## 3213                     287.79070                        3270.3488
## 3214                     287.79070                        3270.3488
## 3215                     287.79070                        3270.3488
## 3216                     287.79070                        3270.3488
## 3217                       0.00000                         109.0116
## 3218                       0.00000                         109.0116
## 3219                       0.00000                         109.0116
## 3220                       0.00000                         109.0116
## 3221                       0.00000                         109.0116
## 3222                       0.00000                         109.0116
## 3223                       0.00000                         109.0116
## 3224                       0.00000                         109.0116
## 3225                       0.00000                         109.0116
##      total_metaecosystem_Tet_indiv  connection ecosystem_size_symmetry set
## 1                         2243.895 unconnected              asymmetric   1
## 2                         2243.895 unconnected              asymmetric   2
## 3                         2243.895 unconnected              asymmetric   3
## 4                         2243.895 unconnected              asymmetric   4
## 5                         2243.895 unconnected              asymmetric   7
## 6                         2243.895 unconnected              asymmetric   8
## 7                         2243.895 unconnected              asymmetric   9
## 8                         2243.895 unconnected              asymmetric  10
## 9                         2243.895 unconnected              asymmetric  11
## 10                        2243.895 unconnected              asymmetric  12
## 11                        2243.895 unconnected              asymmetric  13
## 12                        2243.895 unconnected              asymmetric  14
## 13                        2243.895 unconnected              asymmetric  27
## 14                        2243.895 unconnected              asymmetric  28
## 15                        2243.895 unconnected              asymmetric  29
## 16                        2243.895 unconnected              asymmetric  30
## 17                        2243.895 unconnected              asymmetric  31
## 18                        2243.895 unconnected              asymmetric  32
## 19                        2243.895 unconnected              asymmetric  33
## 20                        2243.895 unconnected              asymmetric  34
## 21                        2243.895 unconnected              asymmetric  37
## 22                        2243.895 unconnected              asymmetric  38
## 23                        2243.895 unconnected              asymmetric  39
## 24                        2243.895 unconnected              asymmetric  40
## 25                           0.000 unconnected              asymmetric   1
## 26                           0.000 unconnected              asymmetric   2
## 27                           0.000 unconnected              asymmetric   3
## 28                           0.000 unconnected              asymmetric   4
## 29                           0.000 unconnected              asymmetric   7
## 30                           0.000 unconnected              asymmetric   8
## 31                           0.000 unconnected              asymmetric   9
## 32                           0.000 unconnected              asymmetric  10
## 33                           0.000 unconnected              asymmetric  11
## 34                           0.000 unconnected              asymmetric  12
## 35                           0.000 unconnected              asymmetric  13
## 36                           0.000 unconnected              asymmetric  14
## 37                           0.000 unconnected              asymmetric  27
## 38                           0.000 unconnected              asymmetric  28
## 39                           0.000 unconnected              asymmetric  29
## 40                           0.000 unconnected              asymmetric  30
## 41                           0.000 unconnected              asymmetric  31
## 42                           0.000 unconnected              asymmetric  32
## 43                           0.000 unconnected              asymmetric  33
## 44                           0.000 unconnected              asymmetric  34
## 45                           0.000 unconnected              asymmetric  37
## 46                           0.000 unconnected              asymmetric  38
## 47                           0.000 unconnected              asymmetric  39
## 48                           0.000 unconnected              asymmetric  40
## 49                           0.000 unconnected              asymmetric   1
## 50                           0.000 unconnected              asymmetric   2
## 51                           0.000 unconnected              asymmetric   3
## 52                           0.000 unconnected              asymmetric   4
## 53                           0.000 unconnected              asymmetric   7
## 54                           0.000 unconnected              asymmetric   8
## 55                           0.000 unconnected              asymmetric   9
## 56                           0.000 unconnected              asymmetric  10
## 57                           0.000 unconnected              asymmetric  11
## 58                           0.000 unconnected              asymmetric  12
## 59                           0.000 unconnected              asymmetric  13
## 60                           0.000 unconnected              asymmetric  14
## 61                           0.000 unconnected              asymmetric  27
## 62                           0.000 unconnected              asymmetric  28
## 63                           0.000 unconnected              asymmetric  29
## 64                           0.000 unconnected              asymmetric  30
## 65                           0.000 unconnected              asymmetric  31
## 66                           0.000 unconnected              asymmetric  32
## 67                           0.000 unconnected              asymmetric  33
## 68                           0.000 unconnected              asymmetric  34
## 69                           0.000 unconnected              asymmetric  37
## 70                           0.000 unconnected              asymmetric  38
## 71                           0.000 unconnected              asymmetric  39
## 72                           0.000 unconnected              asymmetric  40
## 73                           0.000 unconnected              asymmetric   1
## 74                           0.000 unconnected              asymmetric   2
## 75                           0.000 unconnected              asymmetric   3
## 76                           0.000 unconnected              asymmetric   4
## 77                           0.000 unconnected              asymmetric   7
## 78                           0.000 unconnected              asymmetric   8
## 79                           0.000 unconnected              asymmetric   9
## 80                           0.000 unconnected              asymmetric  10
## 81                           0.000 unconnected              asymmetric  11
## 82                           0.000 unconnected              asymmetric  12
## 83                           0.000 unconnected              asymmetric  13
## 84                           0.000 unconnected              asymmetric  14
## 85                           0.000 unconnected              asymmetric  27
## 86                           0.000 unconnected              asymmetric  28
## 87                           0.000 unconnected              asymmetric  29
## 88                           0.000 unconnected              asymmetric  30
## 89                           0.000 unconnected              asymmetric  31
## 90                           0.000 unconnected              asymmetric  32
## 91                           0.000 unconnected              asymmetric  33
## 92                           0.000 unconnected              asymmetric  34
## 93                           0.000 unconnected              asymmetric  37
## 94                           0.000 unconnected              asymmetric  38
## 95                           0.000 unconnected              asymmetric  39
## 96                           0.000 unconnected              asymmetric  40
## 97                           0.000 unconnected              asymmetric   1
## 98                           0.000 unconnected              asymmetric   2
## 99                           0.000 unconnected              asymmetric   3
## 100                          0.000 unconnected              asymmetric   4
## 101                          0.000 unconnected              asymmetric   7
## 102                          0.000 unconnected              asymmetric   8
## 103                          0.000 unconnected              asymmetric   9
## 104                          0.000 unconnected              asymmetric  10
## 105                          0.000 unconnected              asymmetric  11
## 106                          0.000 unconnected              asymmetric  12
## 107                          0.000 unconnected              asymmetric  13
## 108                          0.000 unconnected              asymmetric  14
## 109                          0.000 unconnected              asymmetric  27
## 110                          0.000 unconnected              asymmetric  28
## 111                          0.000 unconnected              asymmetric  29
## 112                          0.000 unconnected              asymmetric  30
## 113                          0.000 unconnected              asymmetric  31
## 114                          0.000 unconnected              asymmetric  32
## 115                          0.000 unconnected              asymmetric  33
## 116                          0.000 unconnected              asymmetric  34
## 117                          0.000 unconnected              asymmetric  37
## 118                          0.000 unconnected              asymmetric  38
## 119                          0.000 unconnected              asymmetric  39
## 120                          0.000 unconnected              asymmetric  40
## 121                          0.000 unconnected              asymmetric   1
## 122                          0.000 unconnected              asymmetric   2
## 123                          0.000 unconnected              asymmetric   3
## 124                          0.000 unconnected              asymmetric   4
## 125                          0.000 unconnected              asymmetric   7
## 126                          0.000 unconnected              asymmetric   8
## 127                          0.000 unconnected              asymmetric   9
## 128                          0.000 unconnected              asymmetric  10
## 129                          0.000 unconnected              asymmetric  11
## 130                          0.000 unconnected              asymmetric  12
## 131                          0.000 unconnected              asymmetric  13
## 132                          0.000 unconnected              asymmetric  14
## 133                          0.000 unconnected              asymmetric  27
## 134                          0.000 unconnected              asymmetric  28
## 135                          0.000 unconnected              asymmetric  29
## 136                          0.000 unconnected              asymmetric  30
## 137                          0.000 unconnected              asymmetric  31
## 138                          0.000 unconnected              asymmetric  32
## 139                          0.000 unconnected              asymmetric  33
## 140                          0.000 unconnected              asymmetric  34
## 141                          0.000 unconnected              asymmetric  37
## 142                          0.000 unconnected              asymmetric  38
## 143                          0.000 unconnected              asymmetric  39
## 144                          0.000 unconnected              asymmetric  40
## 145                          0.000 unconnected              asymmetric   1
## 146                          0.000 unconnected              asymmetric   2
## 147                          0.000 unconnected              asymmetric   3
## 148                          0.000 unconnected              asymmetric   4
## 149                          0.000 unconnected              asymmetric   7
## 150                          0.000 unconnected              asymmetric   8
## 151                          0.000 unconnected              asymmetric   9
## 152                          0.000 unconnected              asymmetric  10
## 153                          0.000 unconnected              asymmetric  11
## 154                          0.000 unconnected              asymmetric  12
## 155                          0.000 unconnected              asymmetric  13
## 156                          0.000 unconnected              asymmetric  14
## 157                          0.000 unconnected              asymmetric  27
## 158                          0.000 unconnected              asymmetric  28
## 159                          0.000 unconnected              asymmetric  29
## 160                          0.000 unconnected              asymmetric  30
## 161                          0.000 unconnected              asymmetric  31
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## 1669                         0.000 unconnected              asymmetric  65
## 1670                         0.000 unconnected              asymmetric  68
## 1671                         0.000 unconnected              asymmetric  69
## 1672                         0.000 unconnected              asymmetric  70
## 1673                         0.000 unconnected              asymmetric  91
## 1674                         0.000 unconnected              asymmetric  92
## 1675                         0.000 unconnected              asymmetric  93
## 1676                         0.000 unconnected              asymmetric  96
## 1677                         0.000 unconnected              asymmetric 105
## 1678                         0.000 unconnected              asymmetric 108
## 1679                         0.000 unconnected              asymmetric 109
## 1680                         0.000 unconnected              asymmetric 110
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## 1685                         0.000 unconnected              asymmetric  25
## 1686                         0.000 unconnected              asymmetric  28
## 1687                         0.000 unconnected              asymmetric  29
## 1688                         0.000 unconnected              asymmetric  30
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## 1690                         0.000 unconnected              asymmetric  52
## 1691                         0.000 unconnected              asymmetric  53
## 1692                         0.000 unconnected              asymmetric  56
## 1693                         0.000 unconnected              asymmetric  65
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## 1695                         0.000 unconnected              asymmetric  69
## 1696                         0.000 unconnected              asymmetric  70
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## 1698                         0.000 unconnected              asymmetric  92
## 1699                         0.000 unconnected              asymmetric  93
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## 1706                         0.000 unconnected              asymmetric  12
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## 1711                         0.000 unconnected              asymmetric  29
## 1712                         0.000 unconnected              asymmetric  30
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## 1714                         0.000 unconnected              asymmetric  52
## 1715                         0.000 unconnected              asymmetric  53
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## 1722                         0.000 unconnected              asymmetric  92
## 1723                         0.000 unconnected              asymmetric  93
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## 1727                         0.000 unconnected              asymmetric 109
## 1728                         0.000 unconnected              asymmetric 110
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## 1730                      2243.895 unconnected              asymmetric   7
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## 1732                      2243.895 unconnected              asymmetric  17
## 1733                      2243.895 unconnected              asymmetric  24
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## 1735                      2243.895 unconnected              asymmetric  34
## 1736                      2243.895 unconnected              asymmetric  37
## 1737                      2243.895 unconnected              asymmetric  44
## 1738                      2243.895 unconnected              asymmetric  47
## 1739                      2243.895 unconnected              asymmetric  54
## 1740                      2243.895 unconnected              asymmetric  57
## 1741                      2243.895 unconnected              asymmetric  64
## 1742                      2243.895 unconnected              asymmetric  67
## 1743                      2243.895 unconnected              asymmetric  74
## 1744                      2243.895 unconnected              asymmetric  77
## 1745                      2243.895 unconnected              asymmetric  84
## 1746                      2243.895 unconnected              asymmetric  87
## 1747                      2243.895 unconnected              asymmetric  94
## 1748                      2243.895 unconnected              asymmetric  97
## 1749                      2243.895 unconnected              asymmetric 104
## 1750                      2243.895 unconnected              asymmetric 107
## 1751                      2243.895 unconnected              asymmetric 114
## 1752                      2243.895 unconnected              asymmetric 117
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## 1795                         0.000 unconnected              asymmetric  94
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## 1799                         0.000 unconnected              asymmetric 114
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## 1807                         0.000 unconnected              asymmetric  34
## 1808                         0.000 unconnected              asymmetric  37
## 1809                         0.000 unconnected              asymmetric  44
## 1810                         0.000 unconnected              asymmetric  47
## 1811                         0.000 unconnected              asymmetric  54
## 1812                         0.000 unconnected              asymmetric  57
## 1813                         0.000 unconnected              asymmetric  64
## 1814                         0.000 unconnected              asymmetric  67
## 1815                         0.000 unconnected              asymmetric  74
## 1816                         0.000 unconnected              asymmetric  77
## 1817                         0.000 unconnected              asymmetric  84
## 1818                         0.000 unconnected              asymmetric  87
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## 1820                         0.000 unconnected              asymmetric  97
## 1821                         0.000 unconnected              asymmetric 104
## 1822                         0.000 unconnected              asymmetric 107
## 1823                         0.000 unconnected              asymmetric 114
## 1824                         0.000 unconnected              asymmetric 117
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## 1922                      2243.895 unconnected              asymmetric  17
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## 1924                      2243.895 unconnected              asymmetric  25
## 1925                      2243.895 unconnected              asymmetric  44
## 1926                      2243.895 unconnected              asymmetric  45
## 1927                      2243.895 unconnected              asymmetric  46
## 1928                      2243.895 unconnected              asymmetric  47
## 1929                      2243.895 unconnected              asymmetric  51
## 1930                      2243.895 unconnected              asymmetric  52
## 1931                      2243.895 unconnected              asymmetric  59
## 1932                      2243.895 unconnected              asymmetric  60
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## 1934                      2243.895 unconnected              asymmetric  80
## 1935                      2243.895 unconnected              asymmetric  81
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## 1938                      2243.895 unconnected              asymmetric 102
## 1939                      2243.895 unconnected              asymmetric 109
## 1940                      2243.895 unconnected              asymmetric 110
## 1941                      2243.895 unconnected              asymmetric 114
## 1942                      2243.895 unconnected              asymmetric 115
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## 1989                         0.000 unconnected              asymmetric 114
## 1990                         0.000 unconnected              asymmetric 115
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## 1995                         0.000 unconnected              asymmetric  24
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## 1998                         0.000 unconnected              asymmetric  45
## 1999                         0.000 unconnected              asymmetric  46
## 2000                         0.000 unconnected              asymmetric  47
## 2001                         0.000 unconnected              asymmetric  51
## 2002                         0.000 unconnected              asymmetric  52
## 2003                         0.000 unconnected              asymmetric  59
## 2004                         0.000 unconnected              asymmetric  60
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## 2006                         0.000 unconnected              asymmetric  80
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## 2008                         0.000 unconnected              asymmetric  82
## 2009                         0.000 unconnected              asymmetric 101
## 2010                         0.000 unconnected              asymmetric 102
## 2011                         0.000 unconnected              asymmetric 109
## 2012                         0.000 unconnected              asymmetric 110
## 2013                         0.000 unconnected              asymmetric 114
## 2014                         0.000 unconnected              asymmetric 115
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## 2019                         0.000 unconnected              asymmetric  24
## 2020                         0.000 unconnected              asymmetric  25
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## 2022                         0.000 unconnected              asymmetric  45
## 2023                         0.000 unconnected              asymmetric  46
## 2024                         0.000 unconnected              asymmetric  47
## 2025                         0.000 unconnected              asymmetric  51
## 2026                         0.000 unconnected              asymmetric  52
## 2027                         0.000 unconnected              asymmetric  59
## 2028                         0.000 unconnected              asymmetric  60
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## 3199                         0.000 unconnected              asymmetric  21
## 3200                         0.000 unconnected              asymmetric  30
## 3201                         0.000 unconnected              asymmetric  31
## 3202                         0.000 unconnected              asymmetric  36
## 3203                         0.000 unconnected              asymmetric  37
## 3204                         0.000 unconnected              asymmetric  38
## 3205                         0.000 unconnected              asymmetric  43
## 3206                         0.000 unconnected              asymmetric  44
## 3207                         0.000 unconnected              asymmetric  45
## 3208                         0.000 unconnected              asymmetric  50
## 3209                         0.000 unconnected              asymmetric  51
## 3210                         0.000 unconnected              asymmetric  60
## 3211                         0.000 unconnected              asymmetric  63
## 3212                         0.000 unconnected              asymmetric  64
## 3213                         0.000 unconnected              asymmetric  65
## 3214                         0.000 unconnected              asymmetric  66
## 3215                         0.000 unconnected              asymmetric  67
## 3216                         0.000 unconnected              asymmetric  68
## 3217                         0.000 unconnected              asymmetric  13
## 3218                         0.000 unconnected              asymmetric  14
## 3219                         0.000 unconnected              asymmetric  15
## 3220                         0.000 unconnected              asymmetric  16
## 3221                         0.000 unconnected              asymmetric  17
## 3222                         0.000 unconnected              asymmetric  18
## 3223                         0.000 unconnected              asymmetric  21
## 3224                         0.000 unconnected              asymmetric  30
## 3225                         0.000 unconnected              asymmetric  31
##      ID_first_ecosystem ID_second_ecosystem
## 1                     1                  11
## 2                     1                  11
## 3                     1                  11
## 4                     1                  11
## 5                     1                  11
## 6                     1                  11
## 7                     1                  11
## 8                     1                  11
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##  [ reached 'max' / getOption("max.print") -- omitted 6695 rows ]
ds_metaecosystems <- ds_metaecosystems %>%
  mutate(
    type = case_when(
      metaecosystem_type == "Small-Large unconnected" ~ "asymmetric",
      metaecosystem_type == "Small-Large meta-ecosystem" ~ "asymmetric",
      metaecosystem_type == "Medium-Medium unconnected" ~ "symmetric",
      metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "symmetric",
      metaecosystem_type == "Small-Small meta-ecosystem" ~ "Small-Small",
      metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "Medium-Medium"
    ))

Filter according to disturbance

Here I’m filtering ecosystems to have only the ones with disturbance high.

#Filter data sets according to the global disturbance
ds_individuals = ds_individuals %>%
  filter(disturbance == disturbance_global_input)
ds_ecosystems = ds_ecosystems %>%
  filter(disturbance == disturbance_global_input)
ds_ecosystems_effect_size = ds_ecosystems_effect_size %>%
  filter(disturbance == disturbance_global_input)
ds_metaecosystems = ds_metaecosystems %>%
  filter(disturbance == disturbance_global_input)
ds_classes = ds_classes %>%
  filter(disturbance == disturbance_global_input)
ds_classes_effect_size = ds_classes_effect_size %>%
  filter(disturbance == disturbance_global_input)

Plots & Analysis

All Meta-ecosystems

metaecosystem_type_i = c("Small-Small meta-ecosystem",
                         "Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Large-Large meta-ecosystem",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Alpha (mean Shannon)

response_variable = "mean_shannon"

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)


Beta (Bray-Curtis)

response_variable = "bray_curtis"

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)
## Warning: Removed 2 rows containing non-finite outside the scale range
## (`stat_summary()`).


Gamma (regional richness)

response_variable = "metaecosystem_richness"

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)


Biomass

response_variable = "total_metaecosystem_bioarea_mm2"

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)


SL vs MM

Alpha (mean Shannon)

response_variable = "mean_shannon"
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)



Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.

SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.2e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e-02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.4e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.1e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -7.2e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.6e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.4e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.8e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.9e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00482332 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.5e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -7.5e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.9e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.6e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.2e+02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.6e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.9e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -8.6e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.4e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.8e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.1e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.6e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0147445 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -7.0e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.3e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.8e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.7   0.061   * weak
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##     system_nr_unconnected_systems  ΔAIC_full
## 1             1030 1031 1037 1044 -3.2658662
## 2             1030 1031 1039 1042 -3.1902927
## 3             1026 1035 1037 1044 -3.1184539
## 4             1026 1035 1039 1042 -3.0498505
## 5             1029 1031 1040 1042 -2.9582525
## 6             1027 1031 1040 1044 -2.9161783
## 7             1029 1035 1036 1042 -2.8370408
## 8             1027 1035 1036 1044 -2.7773951
## 9             1026 1034 1040 1042 -2.7516252
## 10            1029 1031 1037 1045 -2.7318940
## 11            1030 1033 1037 1044 -2.7253151
## 12            1030 1034 1036 1042 -2.7137428
## 13            1030 1032 1036 1044 -2.7114029
## 14            1027 1031 1039 1045 -2.6823829
## 15            1030 1033 1039 1042 -2.6125976
## 16            1026 1032 1040 1044 -2.6074367
## 17            1028 1035 1037 1044 -2.5148704
## 18            1026 1033 1037 1044 -2.5148462
## 19            1026 1034 1037 1045 -2.5107510
## 20            1026 1032 1039 1045 -2.4777456
## 21            1028 1031 1037 1044 -2.4644361
## 22            1028 1035 1039 1042 -2.3997450
## 23            1029 1033 1040 1042 -2.3883546
## 24            1027 1033 1040 1044 -2.3422727
## 25            1026 1033 1039 1042 -2.3223480
## 26            1029 1035 1037 1041 -2.2911892
## 27            1028 1031 1039 1042 -2.2608060
## 28            1029 1033 1037 1045 -2.2388491
## 29            1027 1035 1039 1041 -2.2329835
## 30            1030 1034 1037 1041 -2.1858149
## 31            1030 1033 1036 1044 -2.1815047
## 32            1030 1032 1039 1041 -2.1812818
## 33            1029 1032 1036 1045 -2.1666678
## 34            1027 1034 1036 1045 -2.1360380
## 35            1027 1033 1036 1044 -2.1353277
## 36            1027 1033 1039 1045 -2.1347409
## 37            1028 1032 1040 1044 -2.1315380
## 38            1028 1034 1040 1042 -2.1114067
## 39            1029 1033 1036 1042 -2.1107839
## 40            1026 1033 1040 1044 -2.0926051
## 41            1029 1035 1038 1042 -2.0353298
## 42            1028 1031 1040 1044 -2.0241523
## 43            1028 1035 1036 1044 -1.9870485
## 44            1028 1032 1036 1044 -1.9830983
## 45            1028 1034 1037 1045 -1.9598801
## 46            1026 1033 1039 1045 -1.9486814
## 47            1029 1032 1040 1041 -1.9381692
## 48            1027 1035 1038 1044 -1.9306806
## 49            1030 1032 1038 1044 -1.9295017
## 50            1030 1034 1038 1042 -1.9220500
## 51            1028 1032 1039 1045 -1.9218019
## 52            1030 1031 1038 1044 -1.9169879
## 53            1027 1034 1040 1041 -1.9074780
## 54            1028 1031 1039 1045 -1.8794146
## 55            1027 1031 1038 1044 -1.8782998
## 56            1029 1031 1038 1042 -1.8673505
## 57            1028 1034 1036 1042 -1.8480452
## 58            1026 1035 1038 1044 -1.8019937
## 59            1029 1033 1037 1041 -1.7843168
## 60            1026 1032 1038 1044 -1.7648774
## 61            1030 1033 1039 1041 -1.7338144
## 62            1029 1033 1036 1045 -1.6803511
## 63            1026 1034 1038 1042 -1.6750491
## 64            1027 1033 1039 1041 -1.5668099
## 65            1028 1035 1039 1041 -1.5647583
## 66            1028 1032 1039 1041 -1.5639659
## 67            1030 1033 1036 1042 -1.5109156
## 68            1026 1033 1037 1045 -1.5017169
## 69            1029 1033 1040 1041 -1.4493556
## 70            1029 1032 1038 1045 -1.4477843
## 71            1026 1033 1040 1042 -1.4287577
## 72            1027 1034 1038 1045 -1.4224364
## 73            1028 1034 1036 1045 -1.4035177
## 74            1029 1031 1038 1045 -1.4007823
## 75            1028 1031 1037 1045 -1.3837852
## 76            1028 1031 1040 1042 -1.3837003
## 77            1028 1034 1037 1041 -1.3704474
## 78            1029 1035 1037 1043 -1.3447447
## 79            1028 1035 1036 1042 -1.3379690
## 80            1030 1031 1038 1042 -1.3160477
## 81            1027 1035 1039 1043 -1.2746212
## 82            1030 1032 1039 1043 -1.2667283
## 83            1030 1031 1039 1043 -1.2581718
## 84            1027 1031 1039 1043 -1.2407733
## 85            1030 1034 1037 1043 -1.2155303
## 86            1026 1034 1038 1045 -1.2151508
## 87            1026 1035 1038 1042 -1.2088780
## 88            1029 1031 1037 1043 -1.2066846
## 89            1030 1033 1037 1041 -1.2051259
## 90            1028 1034 1040 1041 -1.1992563
## 91            1026 1032 1039 1043 -1.1679179
## 92            1026 1035 1039 1043 -1.1632386
## 93            1027 1033 1036 1045 -1.1346786
## 94            1029 1035 1038 1041 -1.0874779
## 95            1029 1032 1038 1041 -1.0622404
## 96            1026 1034 1037 1043 -1.0577309
## 97            1029 1032 1040 1043 -1.0517986
## 98            1028 1035 1037 1041 -1.0447430
## 99            1029 1032 1036 1043 -1.0353358
## 100           1027 1034 1040 1043 -1.0231825
## 101           1027 1034 1038 1041 -1.0063826
## 102           1030 1034 1038 1041 -0.9975399
## 103           1029 1031 1040 1043 -0.9887564
## 104           1028 1032 1036 1045 -0.9522282
## 105           1027 1031 1038 1045 -0.9286757
## 106           1027 1033 1040 1041 -0.9069473
## 107           1029 1035 1036 1043 -0.8866580
## 108           1026 1034 1040 1043 -0.8337482
## 109           1027 1034 1036 1043 -0.8147813
## 110           1030 1034 1036 1043 -0.7999913
## 111           1030 1031 1037 1043 -0.7969388
## 112           1026 1032 1038 1045 -0.7962529
## 113           1028 1032 1040 1041 -0.7396395
## 114           1026 1035 1037 1043 -0.7119218
## 115           1027 1035 1038 1041 -0.6161209
## 116           1030 1032 1038 1041 -0.5240635
## 117           1027 1031 1040 1043 -0.5222448
## 118           1027 1035 1036 1043 -0.4430857
## 119           1026 1032 1040 1043 -0.4377593
## 120           1030 1032 1036 1043 -0.3648467

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -3.6   0.019 ** moderate
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##     system_nr_unconnected_systems  ΔAIC_fix
## 1             1030 1031 1037 1044 -5.146101
## 2             1030 1031 1039 1042 -5.072250
## 3             1026 1035 1037 1044 -5.001249
## 4             1026 1035 1039 1042 -4.934501
## 5             1029 1031 1040 1042 -4.847019
## 6             1027 1031 1040 1044 -4.797015
## 7             1029 1035 1036 1042 -4.720641
## 8             1026 1034 1040 1042 -4.640096
## 9             1030 1033 1037 1044 -4.620535
## 10            1029 1031 1037 1045 -4.612677
## 11            1027 1035 1036 1044 -4.598583
## 12            1030 1034 1036 1042 -4.595058
## 13            1027 1031 1039 1045 -4.558706
## 14            1030 1033 1039 1042 -4.509394
## 15            1026 1033 1037 1044 -4.502599
## 16            1026 1032 1040 1044 -4.480598
## 17            1030 1032 1036 1044 -4.458855
## 18            1028 1031 1037 1044 -4.452169
## 19            1028 1035 1037 1044 -4.411982
## 20            1026 1034 1037 1045 -4.391531
## 21            1026 1032 1039 1045 -4.351626
## 22            1026 1033 1039 1042 -4.310219
## 23            1028 1035 1039 1042 -4.298733
## 24            1029 1033 1040 1042 -4.288402
## 25            1028 1031 1039 1042 -4.248685
## 26            1027 1033 1040 1044 -4.236581
## 27            1029 1035 1037 1041 -4.169475
## 28            1029 1033 1037 1045 -4.134178
## 29            1027 1033 1036 1044 -4.121890
## 30            1030 1033 1036 1044 -4.110743
## 31            1029 1033 1036 1042 -4.098189
## 32            1030 1034 1037 1041 -4.060567
## 33            1027 1035 1039 1041 -4.055340
## 34            1029 1032 1036 1045 -4.036830
## 35            1026 1033 1040 1044 -4.026054
## 36            1027 1033 1039 1045 -4.024871
## 37            1028 1032 1040 1044 -4.024487
## 38            1028 1034 1040 1042 -4.012633
## 39            1027 1034 1036 1045 -4.008396
## 40            1028 1032 1036 1044 -3.969436
## 41            1028 1031 1040 1044 -3.957528
## 42            1030 1032 1039 1041 -3.955223
## 43            1029 1035 1038 1042 -3.934064
## 44            1028 1035 1036 1044 -3.917866
## 45            1026 1033 1039 1045 -3.880276
## 46            1029 1031 1038 1042 -3.854964
## 47            1028 1034 1037 1045 -3.854439
## 48            1030 1031 1038 1044 -3.848351
## 49            1028 1034 1036 1042 -3.835532
## 50            1027 1035 1038 1044 -3.818737
## 51            1030 1034 1038 1042 -3.818707
## 52            1029 1032 1040 1041 -3.814186
## 53            1028 1031 1039 1045 -3.810866
## 54            1028 1032 1039 1045 -3.809397
## 55            1027 1031 1038 1044 -3.795204
## 56            1027 1034 1040 1041 -3.785215
## 57            1029 1033 1037 1041 -3.771427
## 58            1026 1032 1038 1044 -3.751469
## 59            1026 1035 1038 1044 -3.734939
## 60            1030 1032 1038 1044 -3.701263
## 61            1027 1033 1039 1041 -3.686460
## 62            1030 1033 1039 1041 -3.663657
## 63            1026 1034 1038 1042 -3.662746
## 64            1029 1033 1036 1045 -3.611549
## 65            1028 1032 1039 1041 -3.550160
## 66            1028 1035 1039 1041 -3.495888
## 67            1030 1033 1036 1042 -3.463478
## 68            1026 1033 1037 1045 -3.456018
## 69            1026 1033 1040 1042 -3.384269
## 70            1029 1033 1040 1041 -3.383492
## 71            1028 1034 1037 1041 -3.356039
## 72            1028 1031 1040 1042 -3.339327
## 73            1028 1031 1037 1045 -3.337990
## 74            1029 1031 1038 1045 -3.334041
## 75            1029 1032 1038 1045 -3.334018
## 76            1028 1034 1036 1045 -3.333319
## 77            1027 1034 1038 1045 -3.308222
## 78            1028 1035 1036 1042 -3.291612
## 79            1030 1031 1038 1042 -3.269202
## 80            1029 1035 1037 1043 -3.235979
## 81            1027 1031 1039 1043 -3.227334
## 82            1029 1031 1037 1043 -3.192817
## 83            1030 1031 1039 1043 -3.176099
## 84            1026 1035 1038 1042 -3.163077
## 85            1027 1035 1039 1043 -3.159892
## 86            1030 1033 1037 1041 -3.157110
## 87            1026 1032 1039 1043 -3.154114
## 88            1026 1034 1038 1045 -3.148024
## 89            1028 1034 1040 1041 -3.131936
## 90            1026 1034 1037 1043 -3.117013
## 91            1030 1034 1037 1043 -3.098275
## 92            1026 1035 1039 1043 -3.094370
## 93            1030 1032 1039 1043 -3.090770
## 94            1027 1033 1036 1045 -3.084860
## 95            1029 1032 1038 1041 -3.048260
## 96            1029 1032 1036 1043 -3.020773
## 97            1029 1035 1038 1041 -3.020002
## 98            1028 1035 1037 1041 -2.997532
## 99            1027 1034 1038 1041 -2.992763
## 100           1029 1032 1040 1043 -2.940788
## 101           1030 1034 1038 1041 -2.927918
## 102           1029 1031 1040 1043 -2.923744
## 103           1027 1034 1040 1043 -2.915505
## 104           1028 1032 1036 1045 -2.901341
## 105           1027 1031 1038 1045 -2.879878
## 106           1027 1033 1040 1041 -2.859200
## 107           1029 1035 1036 1043 -2.817868
## 108           1027 1034 1036 1043 -2.800805
## 109           1026 1034 1040 1043 -2.768333
## 110           1030 1031 1037 1043 -2.748578
## 111           1026 1032 1038 1045 -2.746394
## 112           1030 1034 1036 1043 -2.728791
## 113           1028 1032 1040 1041 -2.690826
## 114           1026 1035 1037 1043 -2.664620
## 115           1027 1035 1038 1041 -2.566863
## 116           1027 1031 1040 1043 -2.473529
## 117           1030 1032 1038 1041 -2.469824
## 118           1027 1035 1036 1043 -2.393025
## 119           1026 1032 1040 1043 -2.389230
## 120           1030 1032 1036 1043 -2.358171
MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.9   0.225     none
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##    system_nr_unconnected_systems  ΔAIC_full
## 1                      1058 1062 -0.4481346
## 2                      1062 1058 -0.4481346
## 3                      1056 1065 -0.4075034
## 4                      1065 1056 -0.4075034
## 5                      1059 1061 -0.1183263
## 6                      1061 1059 -0.1183263
## 7                      1057 1062  0.5109625
## 8                      1062 1057  0.5109625
## 9                      1057 1061  0.5707120
## 10                     1061 1057  0.5707120
## 11                     1056 1064  0.6454787
## 12                     1064 1056  0.6454787
## 13                     1059 1060  0.7472458
## 14                     1060 1059  0.7472458
## 15                     1057 1065  0.7630824
## 16                     1065 1057  0.7630824
## 17                     1058 1060  0.7757166
## 18                     1060 1058  0.7757166
## 19                     1056 1063  1.0166883
## 20                     1063 1056  1.0166883
## 21                     1058 1064  1.1140341
## 22                     1064 1058  1.1140341
## 23                     1059 1063  1.4921890
## 24                     1063 1059  1.4921890
## 25                     1060 1065  1.9526951
## 26                     1065 1060  1.9526951
## 27                     1061 1064  2.0178706
## 28                     1064 1061  2.0178706
## 29                     1062 1063  2.2088481
## 30                     1063 1062  2.2088481

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.6   0.115     none
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##    system_nr_unconnected_systems    ΔAIC_fix
## 1                      1058 1062 -1.59065258
## 2                      1062 1058 -1.59065258
## 3                      1057 1062 -1.42882696
## 4                      1062 1057 -1.42882696
## 5                      1056 1064 -1.28926810
## 6                      1064 1056 -1.28926810
## 7                      1056 1065 -1.28719394
## 8                      1065 1056 -1.28719394
## 9                      1059 1061 -1.28604826
## 10                     1061 1059 -1.28604826
## 11                     1059 1060 -1.20038948
## 12                     1060 1059 -1.20038948
## 13                     1057 1065 -0.73659724
## 14                     1065 1057 -0.73659724
## 15                     1058 1064 -0.62129435
## 16                     1064 1058 -0.62129435
## 17                     1057 1061 -0.25418908
## 18                     1061 1057 -0.25418908
## 19                     1059 1063 -0.16044582
## 20                     1063 1059 -0.16044582
## 21                     1058 1060 -0.11351080
## 22                     1060 1058 -0.11351080
## 23                     1060 1065  0.01814328
## 24                     1065 1060  0.01814328
## 25                     1061 1064  0.08004895
## 26                     1064 1061  0.08004895
## 27                     1056 1063  0.19667134
## 28                     1063 1056  0.19667134
## 29                     1062 1063  0.26649537
## 30                     1063 1062  0.26649537


Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.

Beta (Bray-Curtis)

response_variable = "bray_curtis"
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)


SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.7e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00397541 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -8.8e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.0e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.7e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.3e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.5e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.0e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00280091 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.7e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00259059 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -3.9e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.1e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.9e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e-01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.1e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0111113 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -6.9e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+01
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00233093 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -7.2e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -5.9e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -3.3   0.027 ** moderate
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##     system_nr_unconnected_systems ΔAIC_full
## 1             1027 1033 1040 1044 -5.131031
## 2             1027 1034 1040 1043 -4.977195
## 3             1027 1034 1040 1041 -4.905636
## 4             1027 1031 1040 1044 -4.812797
## 5             1027 1033 1040 1041 -4.717979
## 6             1027 1034 1038 1041 -4.715167
## 7             1027 1034 1036 1045 -4.670136
## 8             1027 1035 1036 1044 -4.662253
## 9             1027 1033 1036 1044 -4.637807
## 10            1027 1034 1036 1043 -4.554477
## 11            1027 1031 1040 1043 -4.474211
## 12            1027 1033 1036 1045 -4.436319
## 13            1027 1033 1039 1045 -4.344398
## 14            1027 1035 1036 1043 -4.315984
## 15            1027 1035 1039 1043 -4.204646
## 16            1027 1035 1039 1041 -4.145796
## 17            1029 1032 1040 1043 -4.133475
## 18            1027 1033 1039 1041 -4.119206
## 19            1029 1032 1040 1041 -4.099971
## 20            1027 1031 1039 1045 -4.065356
## 21            1030 1032 1036 1044 -4.000025
## 22            1029 1033 1040 1041 -3.923811
## 23            1027 1031 1039 1043 -3.877826
## 24            1027 1035 1038 1044 -3.850639
## 25            1029 1032 1036 1045 -3.837177
## 26            1027 1034 1038 1045 -3.836793
## 27            1030 1033 1036 1044 -3.794418
## 28            1029 1031 1040 1043 -3.701014
## 29            1030 1032 1036 1043 -3.683937
## 30            1029 1032 1036 1043 -3.683740
## 31            1028 1032 1040 1044 -3.674511
## 32            1026 1032 1040 1044 -3.632629
## 33            1030 1034 1036 1043 -3.631710
## 34            1030 1032 1039 1043 -3.628881
## 35            1030 1032 1039 1041 -3.617396
## 36            1029 1033 1036 1045 -3.600168
## 37            1026 1033 1040 1044 -3.551073
## 38            1027 1031 1038 1044 -3.539664
## 39            1029 1033 1040 1042 -3.533412
## 40            1027 1035 1038 1041 -3.502220
## 41            1030 1033 1039 1041 -3.479676
## 42            1027 1031 1038 1045 -3.456072
## 43            1029 1035 1036 1043 -3.452945
## 44            1028 1031 1040 1044 -3.447980
## 45            1028 1032 1040 1041 -3.429058
## 46            1028 1034 1040 1041 -3.411945
## 47            1029 1031 1040 1042 -3.403523
## 48            1030 1033 1037 1044 -3.385498
## 49            1026 1032 1040 1043 -3.358420
## 50            1026 1034 1040 1043 -3.345094
## 51            1030 1032 1038 1044 -3.325410
## 52            1030 1031 1037 1044 -3.313350
## 53            1030 1031 1039 1043 -3.283020
## 54            1030 1034 1036 1042 -3.209263
## 55            1030 1034 1037 1041 -3.195463
## 56            1030 1033 1037 1041 -3.186302
## 57            1030 1033 1039 1042 -3.160470
## 58            1030 1033 1036 1042 -3.159552
## 59            1030 1034 1037 1043 -3.155227
## 60            1029 1032 1038 1045 -3.154626
## 61            1029 1033 1037 1045 -3.153191
## 62            1028 1034 1040 1042 -3.143799
## 63            1028 1031 1040 1042 -3.140252
## 64            1026 1033 1040 1042 -3.138249
## 65            1028 1032 1036 1044 -3.137845
## 66            1028 1032 1036 1045 -3.104180
## 67            1026 1034 1040 1042 -3.104065
## 68            1030 1031 1037 1043 -3.085122
## 69            1028 1035 1036 1044 -3.082182
## 70            1028 1032 1039 1045 -3.079951
## 71            1029 1031 1037 1045 -3.079872
## 72            1028 1034 1036 1045 -3.071368
## 73            1030 1031 1038 1044 -3.071277
## 74            1030 1031 1039 1042 -3.066697
## 75            1030 1032 1038 1041 -3.054198
## 76            1026 1032 1039 1045 -3.042656
## 77            1030 1034 1038 1041 -3.017531
## 78            1029 1035 1036 1042 -3.005537
## 79            1029 1035 1037 1041 -2.997568
## 80            1026 1033 1039 1045 -2.978107
## 81            1029 1033 1036 1042 -2.977804
## 82            1029 1035 1037 1043 -2.972028
## 83            1029 1032 1038 1041 -2.943027
## 84            1029 1033 1037 1041 -2.938318
## 85            1028 1031 1039 1045 -2.903679
## 86            1029 1031 1038 1045 -2.859475
## 87            1028 1035 1039 1041 -2.856092
## 88            1028 1032 1039 1041 -2.854888
## 89            1028 1031 1037 1045 -2.854281
## 90            1029 1035 1038 1041 -2.838835
## 91            1029 1031 1037 1043 -2.828815
## 92            1028 1035 1037 1044 -2.819852
## 93            1026 1032 1039 1043 -2.806642
## 94            1026 1033 1037 1045 -2.804241
## 95            1028 1034 1037 1045 -2.795984
## 96            1026 1035 1039 1043 -2.785781
## 97            1026 1035 1037 1044 -2.780723
## 98            1026 1034 1037 1045 -2.754030
## 99            1028 1031 1037 1044 -2.727819
## 100           1030 1034 1038 1042 -2.713690
## 101           1026 1033 1037 1044 -2.711566
## 102           1028 1035 1037 1041 -2.699511
## 103           1030 1031 1038 1042 -2.677046
## 104           1028 1035 1039 1042 -2.634773
## 105           1028 1035 1036 1042 -2.620015
## 106           1026 1035 1039 1042 -2.598459
## 107           1028 1034 1037 1041 -2.577819
## 108           1026 1035 1037 1043 -2.575947
## 109           1028 1034 1036 1042 -2.568613
## 110           1026 1032 1038 1045 -2.565685
## 111           1026 1035 1038 1044 -2.556292
## 112           1026 1032 1038 1044 -2.551427
## 113           1028 1031 1039 1042 -2.549840
## 114           1026 1033 1039 1042 -2.545385
## 115           1026 1034 1038 1045 -2.536037
## 116           1029 1035 1038 1042 -2.516755
## 117           1026 1034 1037 1043 -2.480185
## 118           1029 1031 1038 1042 -2.399991
## 119           1026 1035 1038 1042 -2.226465
## 120           1026 1034 1038 1042 -2.125076

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -4.6   0.012 ** moderate
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##     system_nr_unconnected_systems  ΔAIC_fix
## 1             1027 1033 1040 1044 -6.940532
## 2             1027 1034 1040 1043 -6.903324
## 3             1027 1034 1040 1041 -6.760521
## 4             1027 1034 1038 1041 -6.622166
## 5             1027 1034 1036 1045 -6.606294
## 6             1027 1033 1036 1044 -6.577876
## 7             1027 1035 1036 1044 -6.562129
## 8             1027 1034 1036 1043 -6.549768
## 9             1027 1031 1040 1044 -6.452391
## 10            1027 1033 1040 1041 -6.371757
## 11            1027 1033 1036 1045 -6.220793
## 12            1027 1035 1036 1043 -6.186646
## 13            1027 1033 1039 1045 -6.096878
## 14            1027 1031 1040 1043 -6.057354
## 15            1027 1035 1039 1043 -6.049751
## 16            1029 1032 1040 1043 -5.933082
## 17            1027 1033 1039 1041 -5.930748
## 18            1027 1035 1039 1041 -5.897280
## 19            1029 1032 1040 1041 -5.794994
## 20            1030 1032 1036 1044 -5.757495
## 21            1027 1034 1038 1045 -5.697180
## 22            1027 1035 1038 1044 -5.662918
## 23            1029 1032 1036 1045 -5.651213
## 24            1027 1031 1039 1045 -5.633029
## 25            1027 1031 1039 1043 -5.629971
## 26            1029 1032 1036 1043 -5.617087
## 27            1030 1032 1036 1043 -5.394408
## 28            1030 1032 1039 1043 -5.306848
## 29            1029 1033 1040 1041 -5.292856
## 30            1030 1034 1036 1043 -5.287809
## 31            1027 1031 1038 1044 -5.254627
## 32            1030 1033 1036 1044 -5.254242
## 33            1030 1032 1039 1041 -5.168969
## 34            1028 1032 1040 1044 -5.158396
## 35            1027 1035 1038 1041 -5.156805
## 36            1026 1032 1040 1044 -5.142217
## 37            1029 1033 1036 1045 -5.138453
## 38            1029 1035 1036 1043 -5.113887
## 39            1029 1031 1040 1043 -4.984868
## 40            1030 1032 1038 1044 -4.955229
## 41            1027 1031 1038 1045 -4.902859
## 42            1029 1032 1038 1045 -4.853952
## 43            1028 1032 1036 1044 -4.840536
## 44            1026 1032 1040 1043 -4.801060
## 45            1026 1034 1040 1043 -4.726029
## 46            1026 1033 1040 1044 -4.691634
## 47            1028 1032 1040 1041 -4.676531
## 48            1030 1033 1039 1041 -4.663205
## 49            1029 1032 1038 1041 -4.619450
## 50            1028 1034 1040 1041 -4.596171
## 51            1028 1032 1036 1045 -4.535937
## 52            1029 1033 1040 1042 -4.504157
## 53            1028 1032 1039 1045 -4.479165
## 54            1030 1032 1038 1041 -4.472011
## 55            1026 1032 1039 1045 -4.470568
## 56            1026 1032 1039 1043 -4.444710
## 57            1028 1034 1036 1045 -4.442180
## 58            1028 1035 1036 1044 -4.379247
## 59            1030 1031 1039 1043 -4.376579
## 60            1030 1034 1036 1042 -4.375624
## 61            1030 1034 1038 1041 -4.374437
## 62            1030 1034 1037 1043 -4.364962
## 63            1028 1032 1039 1041 -4.338405
## 64            1030 1033 1037 1044 -4.327466
## 65            1028 1031 1040 1044 -4.267812
## 66            1029 1033 1036 1042 -4.263918
## 67            1030 1034 1037 1041 -4.212466
## 68            1029 1033 1037 1045 -4.209670
## 69            1029 1035 1038 1041 -4.208528
## 70            1029 1035 1037 1043 -4.198452
## 71            1029 1035 1036 1042 -4.186153
## 72            1026 1032 1038 1044 -4.139370
## 73            1029 1033 1037 1041 -4.099395
## 74            1030 1031 1038 1044 -4.095837
## 75            1029 1031 1040 1042 -4.063453
## 76            1029 1035 1037 1041 -4.035656
## 77            1026 1033 1039 1045 -4.016902
## 78            1026 1035 1039 1043 -3.994497
## 79            1029 1031 1038 1045 -3.981474
## 80            1030 1031 1037 1044 -3.955214
## 81            1030 1033 1036 1042 -3.932411
## 82            1030 1033 1039 1042 -3.903767
## 83            1026 1034 1040 1042 -3.899653
## 84            1029 1031 1037 1043 -3.897016
## 85            1028 1034 1040 1042 -3.887318
## 86            1028 1035 1039 1041 -3.849173
## 87            1026 1032 1038 1045 -3.846206
## 88            1029 1031 1037 1045 -3.834051
## 89            1030 1033 1037 1041 -3.795195
## 90            1026 1034 1038 1045 -3.755427
## 91            1026 1035 1038 1044 -3.696892
## 92            1030 1034 1038 1042 -3.656193
## 93            1028 1034 1036 1042 -3.649720
## 94            1026 1034 1037 1043 -3.646837
## 95            1026 1034 1037 1045 -3.620843
## 96            1026 1033 1037 1044 -3.612827
## 97            1028 1034 1037 1045 -3.610219
## 98            1028 1031 1039 1045 -3.606477
## 99            1030 1031 1037 1043 -3.599894
## 100           1026 1035 1037 1044 -3.563164
## 101           1028 1035 1037 1044 -3.549454
## 102           1028 1034 1037 1041 -3.503951
## 103           1029 1035 1038 1042 -3.482353
## 104           1026 1033 1040 1042 -3.482214
## 105           1030 1031 1039 1042 -3.478937
## 106           1028 1031 1037 1044 -3.273757
## 107           1026 1033 1039 1042 -3.244087
## 108           1026 1033 1037 1045 -3.243225
## 109           1026 1035 1037 1043 -3.240657
## 110           1029 1031 1038 1042 -3.184571
## 111           1026 1035 1039 1042 -3.170945
## 112           1028 1035 1036 1042 -3.165473
## 113           1028 1035 1039 1042 -3.153646
## 114           1028 1035 1037 1041 -3.060612
## 115           1028 1031 1040 1042 -3.048588
## 116           1026 1034 1038 1042 -3.025000
## 117           1028 1031 1037 1045 -2.878668
## 118           1028 1031 1039 1042 -2.857615
## 119           1030 1031 1038 1042 -2.833675
## 120           1026 1035 1038 1042 -2.557163
MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222507 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222133 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222507 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222133 (tol = 0.002, component 1)
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+02
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.1   0.469     none
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##    system_nr_unconnected_systems  ΔAIC_full
## 1                      1059 1061 -2.1634950
## 2                      1061 1059 -2.1634950
## 3                      1061 1064  0.3104198
## 4                      1064 1061  0.3104198
## 5                      1058 1062  0.6299275
## 6                      1062 1058  0.6299275
## 7                      1058 1064  1.4703315
## 8                      1064 1058  1.4703315
## 9                      1059 1060  1.8363618
## 10                     1060 1059  1.8363618
## 11                     1056 1065  2.3113527
## 12                     1065 1056  2.3113527
## 13                     1056 1064  2.4258678
## 14                     1064 1056  2.4258678
## 15                     1057 1062  2.8145259
## 16                     1062 1057  2.8145259
## 17                     1059 1063  2.9451644
## 18                     1063 1059  2.9451644
## 19                     1058 1060  2.9492200
## 20                     1060 1058  2.9492200
## 21                     1057 1061  2.9921157
## 22                     1061 1057  2.9921157
## 23                     1062 1063  3.0082645
## 24                     1063 1062  3.0082645
## 25                     1060 1065  3.1739693
## 26                     1065 1060  3.1739693
## 27                     1056 1063  3.3683048
## 28                     1063 1056  3.3683048
## 29                     1057 1065  3.5740379
## 30                     1065 1057  3.5740379

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.7   0.333     none
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##    system_nr_unconnected_systems   ΔAIC_fix
## 1                      1059 1061 -1.8677401
## 2                      1061 1059 -1.8677401
## 3                      1058 1062 -1.3609533
## 4                      1062 1058 -1.3609533
## 5                      1061 1064  0.3699422
## 6                      1064 1061  0.3699422
## 7                      1058 1064  0.6864549
## 8                      1064 1058  0.6864549
## 9                      1059 1060  0.7170381
## 10                     1060 1059  0.7170381
## 11                     1056 1065  0.8343727
## 12                     1065 1056  0.8343727
## 13                     1058 1060  0.9528356
## 14                     1060 1058  0.9528356
## 15                     1057 1062  0.9795774
## 16                     1062 1057  0.9795774
## 17                     1057 1061  0.9976548
## 18                     1061 1057  0.9976548
## 19                     1056 1064  1.1258105
## 20                     1064 1056  1.1258105
## 21                     1059 1063  1.2673148
## 22                     1063 1059  1.2673148
## 23                     1062 1063  1.2753382
## 24                     1063 1062  1.2753382
## 25                     1056 1063  1.5564216
## 26                     1063 1056  1.5564216
## 27                     1060 1065  1.7486191
## 28                     1065 1060  1.7486191
## 29                     1057 1065  1.8526093
## 30                     1065 1057  1.8526093


Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.

Gamma (regional richness)

response_variable = "metaecosystem_richness"
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)


SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.2   0.449     none
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##     system_nr_unconnected_systems ΔAIC_full
## 1             1027 1031 1040 1043 0.1184054
## 2             1026 1032 1040 1043 0.4857987
## 3             1030 1032 1036 1043 0.5916539
## 4             1027 1035 1036 1043 0.5916539
## 5             1027 1033 1036 1045 0.6185128
## 6             1027 1033 1040 1041 0.6262096
## 7             1026 1035 1037 1043 0.8013854
## 8             1027 1031 1038 1045 0.8028149
## 9             1030 1031 1037 1043 0.8234183
## 10            1028 1032 1036 1045 0.8765712
## 11            1028 1032 1040 1041 0.9116171
## 12            1026 1033 1037 1045 0.9247340
## 13            1028 1031 1037 1045 0.9435650
## 14            1026 1032 1038 1045 0.9707246
## 15            1028 1031 1040 1042 1.0032662
## 16            1026 1033 1040 1042 1.0124658
## 17            1026 1035 1038 1042 1.0483023
## 18            1028 1035 1037 1041 1.0531285
## 19            1027 1035 1038 1041 1.1313847
## 20            1030 1032 1038 1041 1.1313847
## 21            1030 1031 1038 1042 1.1415923
## 22            1030 1033 1037 1041 1.1415923
## 23            1028 1035 1036 1042 1.1817598
## 24            1030 1033 1036 1042 1.2068920
## 25            1029 1031 1040 1043 1.4738514
## 26            1026 1033 1040 1044 1.6449245
## 27            1028 1031 1040 1044 1.6888776
## 28            1029 1033 1036 1045 1.6953488
## 29            1029 1035 1036 1043 1.6965544
## 30            1026 1035 1038 1044 1.7039081
## 31            1029 1033 1040 1041 1.7112135
## 32            1029 1031 1038 1045 1.7171764
## 33            1030 1033 1036 1044 1.7401448
## 34            1030 1031 1038 1044 1.7500094
## 35            1027 1033 1036 1044 1.7719847
## 36            1029 1032 1036 1043 1.8089431
## 37            1029 1035 1038 1041 1.8187599
## 38            1028 1035 1036 1044 1.8392635
## 39            1027 1031 1039 1043 1.8578998
## 40            1026 1034 1038 1045 1.9171187
## 41            1030 1031 1039 1043 1.9248196
## 42            1026 1034 1040 1043 1.9751176
## 43            1026 1035 1039 1043 2.0164777
## 44            1027 1031 1038 1044 2.0304657
## 45            1026 1033 1039 1045 2.0546512
## 46            1028 1032 1036 1044 2.0694046
## 47            1030 1034 1038 1041 2.0694600
## 48            1030 1034 1036 1043 2.0904245
## 49            1028 1031 1039 1045 2.0907961
## 50            1028 1034 1036 1045 2.1082731
## 51            1030 1033 1039 1041 2.1379006
## 52            1028 1034 1040 1041 2.1437119
## 53            1029 1031 1037 1043 2.1498037
## 54            1027 1033 1040 1044 2.1523181
## 55            1026 1032 1039 1043 2.1720464
## 56            1029 1032 1040 1043 2.1774126
## 57            1027 1033 1039 1041 2.1984253
## 58            1026 1033 1037 1044 2.2119163
## 59            1026 1032 1038 1044 2.2222913
## 60            1028 1035 1039 1041 2.2389915
## 61            1029 1033 1036 1042 2.2627048
## 62            1027 1034 1036 1043 2.2640377
## 63            1029 1032 1038 1041 2.2653341
## 64            1028 1031 1037 1044 2.2727205
## 65            1029 1031 1038 1042 2.2920731
## 66            1029 1033 1037 1041 2.2920731
## 67            1026 1034 1037 1043 2.4002606
## 68            1026 1034 1038 1042 2.4401378
## 69            1028 1032 1039 1041 2.4419863
## 70            1028 1032 1040 1044 2.4485679
## 71            1028 1034 1037 1041 2.5024721
## 72            1027 1033 1039 1045 2.5293857
## 73            1026 1033 1039 1042 2.5511370
## 74            1027 1035 1039 1043 2.5643376
## 75            1030 1032 1039 1043 2.5643376
## 76            1028 1031 1039 1042 2.5780819
## 77            1027 1034 1038 1041 2.5811953
## 78            1027 1034 1040 1043 2.5913595
## 79            1028 1034 1036 1042 2.6035722
## 80            1029 1032 1038 1045 2.6456581
## 81            1029 1033 1040 1042 2.6577686
## 82            1029 1035 1037 1043 2.6591291
## 83            1030 1032 1038 1044 2.6712469
## 84            1027 1035 1038 1044 2.6712469
## 85            1029 1033 1037 1045 2.6896263
## 86            1030 1033 1037 1044 2.7148934
## 87            1028 1035 1037 1044 2.7328657
## 88            1029 1035 1038 1042 2.7658189
## 89            1028 1032 1039 1045 2.7744574
## 90            1028 1034 1037 1045 2.8568194
## 91            1030 1034 1037 1043 2.8772512
## 92            1030 1034 1038 1042 2.9228228
## 93            1027 1034 1038 1045 2.9266862
## 94            1030 1033 1039 1042 2.9600778
## 95            1028 1034 1040 1042 2.9759999
## 96            1028 1035 1039 1042 3.0345699
## 97            1027 1031 1040 1044 3.0487703
## 98            1026 1034 1037 1045 3.2227518
## 99            1026 1035 1037 1044 3.2254653
## 100           1026 1032 1040 1044 3.2793631
## 101           1029 1032 1040 1041 3.3026595
## 102           1029 1032 1036 1045 3.3026595
## 103           1027 1031 1039 1045 3.3100834
## 104           1027 1035 1036 1044 3.3277203
## 105           1030 1032 1036 1044 3.3277203
## 106           1029 1035 1037 1041 3.3536689
## 107           1029 1031 1037 1045 3.3754843
## 108           1030 1034 1037 1041 3.3859468
## 109           1030 1031 1037 1044 3.3985584
## 110           1029 1031 1040 1042 3.4247298
## 111           1026 1032 1039 1045 3.4830031
## 112           1026 1034 1040 1042 3.4877050
## 113           1029 1035 1036 1042 3.5066722
## 114           1026 1035 1039 1042 3.5081735
## 115           1027 1034 1036 1045 3.5265898
## 116           1030 1032 1039 1041 3.5265898
## 117           1027 1035 1039 1041 3.5265898
## 118           1027 1034 1040 1041 3.5265898
## 119           1030 1031 1039 1042 3.5793863
## 120           1030 1034 1036 1042 3.5994587

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.7   0.318     none
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##     system_nr_unconnected_systems    ΔAIC_fix
## 1             1027 1031 1040 1043 -1.65718236
## 2             1027 1033 1036 1045 -1.12259736
## 3             1027 1033 1040 1041 -1.11490052
## 4             1030 1032 1036 1043 -1.05919932
## 5             1027 1035 1036 1043 -1.05919932
## 6             1026 1032 1040 1043 -1.04956469
## 7             1027 1031 1038 1045 -0.66691460
## 8             1028 1032 1036 1045 -0.60753760
## 9             1028 1032 1040 1041 -0.59117420
## 10            1027 1033 1036 1044 -0.16441858
## 11            1027 1035 1038 1041 -0.16035273
## 12            1030 1032 1038 1041 -0.16035273
## 13            1026 1032 1038 1045 -0.15068719
## 14            1030 1031 1037 1043 -0.13808816
## 15            1026 1033 1040 1042 -0.13712296
## 16            1028 1031 1040 1042 -0.12343883
## 17            1030 1033 1036 1042 -0.10750634
## 18            1027 1031 1039 1043 -0.08266643
## 19            1029 1032 1036 1043 -0.07728127
## 20            1029 1031 1040 1043 -0.05377605
## 21            1027 1033 1040 1044  0.16866674
## 22            1029 1033 1036 1045  0.21963355
## 23            1029 1032 1040 1043  0.22264762
## 24            1029 1033 1040 1041  0.23549825
## 25            1030 1031 1038 1042  0.24054564
## 26            1030 1033 1037 1041  0.24054564
## 27            1026 1033 1037 1045  0.24074956
## 28            1027 1031 1038 1044  0.24477102
## 29            1030 1033 1036 1044  0.24725672
## 30            1028 1032 1036 1044  0.26982886
## 31            1027 1033 1039 1041  0.27946580
## 32            1028 1035 1036 1042  0.28071311
## 33            1026 1033 1040 1044  0.28834590
## 34            1028 1031 1037 1045  0.29106203
## 35            1028 1031 1040 1044  0.30541988
## 36            1026 1035 1037 1043  0.30952771
## 37            1029 1035 1036 1043  0.34596173
## 38            1026 1032 1039 1043  0.36299333
## 39            1027 1034 1036 1043  0.40380312
## 40            1030 1031 1039 1043  0.41788013
## 41            1028 1032 1040 1044  0.55483412
## 42            1027 1033 1039 1045  0.55688420
## 43            1029 1033 1036 1042  0.60427912
## 44            1029 1032 1038 1041  0.61624107
## 45            1029 1031 1038 1045  0.61937207
## 46            1030 1031 1038 1044  0.62186766
## 47            1027 1035 1039 1043  0.62481978
## 48            1030 1032 1039 1043  0.62481978
## 49            1026 1035 1038 1042  0.62533298
## 50            1027 1034 1040 1043  0.65487306
## 51            1026 1032 1038 1044  0.65551858
## 52            1028 1032 1039 1041  0.65964771
## 53            1028 1035 1037 1041  0.67724089
## 54            1028 1035 1036 1044  0.68283289
## 55            1030 1033 1039 1041  0.69260830
## 56            1026 1033 1039 1045  0.71993955
## 57            1028 1031 1039 1045  0.72958735
## 58            1029 1031 1037 1043  0.73056357
## 59            1030 1034 1036 1043  0.78930670
## 60            1026 1035 1039 1043  0.81408505
## 61            1026 1034 1040 1043  0.82276296
## 62            1029 1032 1038 1045  0.86936025
## 63            1029 1033 1040 1042  0.87467163
## 64            1030 1032 1038 1044  0.88814996
## 65            1027 1035 1038 1044  0.88814996
## 66            1028 1032 1039 1045  0.90080080
## 67            1029 1031 1038 1042  0.93786621
## 68            1029 1033 1037 1041  0.93786621
## 69            1029 1035 1038 1041  0.94861787
## 70            1027 1034 1038 1041  0.97315483
## 71            1026 1033 1037 1044  0.98256355
## 72            1026 1035 1038 1044  1.00185638
## 73            1028 1031 1037 1044  1.01488846
## 74            1026 1033 1039 1042  1.01902222
## 75            1028 1031 1039 1042  1.02881099
## 76            1028 1034 1036 1045  1.03825704
## 77            1027 1031 1040 1044  1.04877028
## 78            1028 1034 1040 1041  1.05277914
## 79            1028 1035 1039 1041  1.07471304
## 80            1029 1033 1037 1045  1.16109065
## 81            1030 1033 1037 1044  1.17068843
## 82            1027 1034 1038 1045  1.18601448
## 83            1030 1033 1039 1042  1.20764640
## 84            1029 1035 1037 1043  1.24335157
## 85            1030 1034 1038 1041  1.26608050
## 86            1028 1034 1036 1042  1.28287675
## 87            1027 1031 1039 1045  1.31211837
## 88            1026 1034 1038 1045  1.31901954
## 89            1029 1032 1040 1041  1.32074576
## 90            1029 1032 1036 1045  1.32074576
## 91            1026 1032 1040 1044  1.32900261
## 92            1027 1035 1036 1044  1.34515254
## 93            1030 1032 1036 1044  1.34515254
## 94            1026 1034 1037 1043  1.38664507
## 95            1029 1035 1038 1042  1.41161197
## 96            1028 1034 1040 1042  1.47078486
## 97            1028 1035 1037 1044  1.48160821
## 98            1028 1035 1039 1042  1.49063338
## 99            1030 1034 1037 1043  1.51063165
## 100           1026 1034 1038 1042  1.51519213
## 101           1026 1032 1039 1045  1.55016501
## 102           1029 1031 1040 1042  1.55227262
## 103           1028 1034 1037 1041  1.55503012
## 104           1027 1034 1036 1045  1.55803538
## 105           1030 1032 1039 1041  1.55803538
## 106           1027 1035 1039 1041  1.55803538
## 107           1027 1034 1040 1041  1.55803538
## 108           1030 1034 1038 1042  1.62528090
## 109           1028 1034 1037 1045  1.69248914
## 110           1029 1031 1037 1045  1.72370911
## 111           1030 1031 1037 1044  1.73388560
## 112           1030 1031 1039 1042  1.73759816
## 113           1029 1035 1036 1042  1.74052995
## 114           1029 1035 1037 1041  1.86624986
## 115           1026 1035 1037 1044  1.86807498
## 116           1026 1034 1040 1042  1.86966260
## 117           1030 1034 1036 1042  1.87287701
## 118           1026 1035 1039 1042  1.87634137
## 119           1026 1034 1037 1045  1.95401191
## 120           1030 1034 1037 1041  1.95521289
MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.8   0.576     none
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##    system_nr_unconnected_systems ΔAIC_full
## 1                      1057 1062  1.295857
## 2                      1062 1057  1.295857
## 3                      1059 1060  1.891039
## 4                      1060 1059  1.891039
## 5                      1058 1062  2.005519
## 6                      1062 1058  2.005519
## 7                      1056 1064  2.007075
## 8                      1064 1056  2.007075
## 9                      1062 1063  2.635024
## 10                     1063 1062  2.635024
## 11                     1058 1064  2.758295
## 12                     1064 1058  2.758295
## 13                     1060 1065  2.918645
## 14                     1065 1060  2.918645
## 15                     1059 1061  3.032444
## 16                     1059 1063  3.032444
## 17                     1061 1059  3.032444
## 18                     1063 1059  3.032444
## 19                     1057 1065  3.102242
## 20                     1065 1057  3.102242
## 21                     1058 1060  3.125725
## 22                     1060 1058  3.125725
## 23                     1056 1065  3.199072
## 24                     1065 1056  3.199072
## 25                     1061 1064  3.286048
## 26                     1064 1061  3.286048
## 27                     1057 1061  3.772903
## 28                     1061 1057  3.772903
## 29                     1056 1063  3.782587
## 30                     1063 1056  3.782587

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.5    0.62     none
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##    system_nr_unconnected_systems   ΔAIC_fix
## 1                      1058 1062 0.02558494
## 2                      1062 1058 0.02558494
## 3                      1058 1064 0.76954896
## 4                      1064 1058 0.76954896
## 5                      1059 1060 1.13564061
## 6                      1060 1059 1.13564061
## 7                      1059 1061 1.14448056
## 8                      1059 1063 1.14448056
## 9                      1061 1059 1.14448056
## 10                     1063 1059 1.14448056
## 11                     1058 1060 1.20081237
## 12                     1060 1058 1.20081237
## 13                     1062 1063 1.61235729
## 14                     1063 1062 1.61235729
## 15                     1057 1062 1.79492711
## 16                     1062 1057 1.79492711
## 17                     1057 1065 1.92328025
## 18                     1065 1057 1.92328025
## 19                     1061 1064 1.94501477
## 20                     1064 1061 1.94501477
## 21                     1056 1065 1.96756892
## 22                     1065 1056 1.96756892
## 23                     1056 1064 1.99173842
## 24                     1064 1056 1.99173842
## 25                     1056 1063 1.99458722
## 26                     1063 1056 1.99458722
## 27                     1060 1065 1.99783118
## 28                     1065 1060 1.99783118
## 29                     1057 1061 1.99859706
## 30                     1061 1057 1.99859706

Biomass

response_variable = "total_metaecosystem_bioarea_mm2"
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:

plot.metaecos.points(ds_metaecosystems,
                     metaecosystem_type_i,
                     response_variable,
                     3)

Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
                         metaecosystem_type_i,
                         response_variable)



Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.

SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
                         "Small-Large unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -5.1   0.011 ** moderate
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##     system_nr_unconnected_systems ΔAIC_full
## 1             1029 1035 1038 1042 -6.022025
## 2             1028 1035 1039 1042 -6.009392
## 3             1029 1032 1038 1045 -5.980998
## 4             1028 1035 1036 1042 -5.971627
## 5             1028 1032 1039 1045 -5.968418
## 6             1029 1035 1037 1043 -5.964009
## 7             1030 1032 1039 1043 -5.953994
## 8             1030 1033 1039 1042 -5.952080
## 9             1027 1035 1039 1043 -5.950406
## 10            1026 1035 1038 1042 -5.949312
## 11            1030 1032 1038 1044 -5.935165
## 12            1030 1034 1038 1042 -5.933681
## 13            1027 1035 1038 1041 -5.932083
## 14            1028 1035 1037 1041 -5.932061
## 15            1027 1035 1036 1043 -5.931435
## 16            1028 1035 1037 1044 -5.931425
## 17            1027 1035 1038 1044 -5.930187
## 18            1028 1032 1036 1045 -5.929937
## 19            1029 1033 1037 1045 -5.922847
## 20            1029 1032 1040 1043 -5.915603
## 21            1029 1033 1040 1042 -5.913018
## 22            1027 1033 1039 1045 -5.911002
## 23            1026 1035 1037 1043 -5.910253
## 24            1026 1032 1038 1045 -5.907733
## 25            1028 1034 1037 1045 -5.891026
## 26            1027 1034 1038 1045 -5.890883
## 27            1027 1033 1036 1045 -5.890744
## 28            1030 1032 1036 1043 -5.885985
## 29            1030 1032 1038 1041 -5.885243
## 30            1028 1032 1040 1044 -5.884380
## 31            1030 1033 1036 1042 -5.882925
## 32            1028 1034 1040 1042 -5.882767
## 33            1030 1033 1037 1044 -5.875438
## 34            1030 1034 1037 1043 -5.875257
## 35            1027 1031 1038 1045 -5.873727
## 36            1028 1031 1037 1045 -5.873315
## 37            1026 1033 1037 1045 -5.870195
## 38            1030 1031 1038 1042 -5.864916
## 39            1028 1032 1040 1041 -5.845141
## 40            1030 1033 1037 1041 -5.842017
## 41            1030 1031 1037 1043 -5.826602
## 42            1027 1033 1040 1044 -5.826177
## 43            1027 1034 1040 1043 -5.825908
## 44            1028 1031 1040 1042 -5.825505
## 45            1026 1032 1040 1043 -5.825061
## 46            1026 1033 1040 1042 -5.823777
## 47            1027 1033 1040 1041 -5.805192
## 48            1027 1031 1040 1043 -5.789613
## 49            1029 1035 1036 1042 -5.251301
## 50            1029 1035 1037 1041 -5.214670
## 51            1029 1032 1036 1045 -5.213476
## 52            1026 1035 1039 1042 -5.206071
## 53            1030 1032 1039 1041 -5.199912
## 54            1027 1035 1039 1041 -5.195244
## 55            1030 1031 1039 1042 -5.186668
## 56            1029 1032 1040 1041 -5.170284
## 57            1030 1034 1036 1042 -5.168899
## 58            1026 1032 1039 1045 -5.168465
## 59            1029 1031 1037 1045 -5.165148
## 60            1030 1032 1036 1044 -5.161803
## 61            1029 1031 1040 1042 -5.156784
## 62            1027 1035 1036 1044 -5.155613
## 63            1027 1031 1039 1045 -5.146903
## 64            1030 1034 1037 1041 -5.131450
## 65            1026 1035 1037 1044 -5.130977
## 66            1027 1034 1036 1045 -5.127348
## 67            1030 1031 1037 1044 -5.112757
## 68            1026 1034 1037 1045 -5.102779
## 69            1026 1034 1040 1042 -5.096091
## 70            1026 1032 1040 1044 -5.088332
## 71            1027 1034 1040 1041 -5.084501
## 72            1027 1031 1040 1044 -5.065938
## 73            1029 1033 1036 1042 -4.434082
## 74            1029 1031 1038 1042 -4.432915
## 75            1029 1032 1038 1041 -4.430208
## 76            1028 1031 1039 1042 -4.415847
## 77            1028 1032 1039 1041 -4.412631
## 78            1029 1032 1036 1043 -4.405513
## 79            1029 1033 1037 1041 -4.405467
## 80            1029 1031 1037 1043 -4.381131
## 81            1028 1034 1036 1042 -4.376436
## 82            1026 1033 1039 1042 -4.374303
## 83            1027 1033 1039 1041 -4.367195
## 84            1028 1032 1036 1044 -4.349511
## 85            1028 1034 1037 1041 -4.348239
## 86            1026 1032 1039 1043 -4.344340
## 87            1027 1031 1039 1043 -4.342572
## 88            1026 1034 1038 1042 -4.333840
## 89            1027 1034 1038 1041 -4.326583
## 90            1028 1031 1037 1044 -4.326530
## 91            1026 1032 1038 1044 -4.306005
## 92            1027 1031 1038 1044 -4.304605
## 93            1027 1033 1036 1044 -4.304519
## 94            1029 1033 1036 1045 -4.304489
## 95            1027 1034 1036 1043 -4.301859
## 96            1029 1035 1038 1041 -4.301289
## 97            1029 1035 1036 1043 -4.296825
## 98            1028 1035 1039 1041 -4.295904
## 99            1029 1031 1038 1045 -4.292952
## 100           1028 1031 1039 1045 -4.287696
## 101           1026 1033 1037 1044 -4.284830
## 102           1026 1034 1037 1043 -4.282201
## 103           1026 1033 1039 1045 -4.273499
## 104           1026 1035 1039 1043 -4.265870
## 105           1028 1035 1036 1044 -4.244515
## 106           1028 1034 1036 1045 -4.241291
## 107           1029 1033 1040 1041 -4.224922
## 108           1030 1033 1039 1041 -4.222213
## 109           1026 1035 1038 1044 -4.218484
## 110           1026 1034 1038 1045 -4.215300
## 111           1029 1031 1040 1043 -4.209660
## 112           1030 1031 1039 1043 -4.206887
## 113           1030 1033 1036 1044 -4.173196
## 114           1030 1034 1038 1041 -4.166109
## 115           1028 1034 1040 1041 -4.163908
## 116           1030 1031 1038 1044 -4.161992
## 117           1030 1034 1036 1043 -4.161909
## 118           1028 1031 1040 1044 -4.159809
## 119           1026 1033 1040 1044 -4.146483
## 120           1026 1034 1040 1043 -4.135442

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -6.9   0.003 *** strong
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##     system_nr_unconnected_systems  ΔAIC_fix
## 1             1028 1035 1036 1042 -7.963705
## 2             1029 1035 1038 1042 -7.944556
## 3             1026 1035 1038 1042 -7.941393
## 4             1028 1035 1039 1042 -7.932491
## 5             1028 1035 1037 1041 -7.923836
## 6             1027 1035 1038 1041 -7.923739
## 7             1027 1035 1036 1043 -7.923088
## 8             1028 1032 1036 1045 -7.921975
## 9             1029 1032 1038 1045 -7.903120
## 10            1026 1035 1037 1043 -7.902029
## 11            1026 1032 1038 1045 -7.899773
## 12            1028 1032 1039 1045 -7.891113
## 13            1029 1035 1037 1043 -7.883289
## 14            1027 1033 1036 1045 -7.882434
## 15            1030 1032 1036 1043 -7.877800
## 16            1030 1032 1038 1041 -7.877061
## 17            1030 1033 1036 1042 -7.874818
## 18            1030 1032 1039 1043 -7.874419
## 19            1030 1033 1039 1042 -7.873254
## 20            1027 1035 1039 1043 -7.869099
## 21            1027 1031 1038 1045 -7.865420
## 22            1028 1031 1037 1045 -7.865127
## 23            1026 1033 1037 1045 -7.862007
## 24            1030 1032 1038 1044 -7.857041
## 25            1030 1031 1038 1042 -7.856812
## 26            1030 1034 1038 1042 -7.855904
## 27            1028 1035 1037 1044 -7.852789
## 28            1027 1035 1038 1044 -7.850394
## 29            1029 1033 1037 1045 -7.842469
## 30            1028 1032 1040 1041 -7.837021
## 31            1029 1032 1040 1043 -7.836058
## 32            1029 1033 1040 1042 -7.834225
## 33            1030 1033 1037 1041 -7.833593
## 34            1027 1033 1039 1045 -7.830037
## 35            1030 1031 1037 1043 -7.818179
## 36            1028 1031 1040 1042 -7.817462
## 37            1026 1032 1040 1043 -7.816942
## 38            1026 1033 1040 1042 -7.815735
## 39            1028 1034 1037 1045 -7.812332
## 40            1027 1034 1038 1045 -7.811026
## 41            1028 1032 1040 1044 -7.806862
## 42            1028 1034 1040 1042 -7.805594
## 43            1027 1033 1040 1041 -7.796711
## 44            1030 1033 1037 1044 -7.794803
## 45            1030 1034 1037 1043 -7.794217
## 46            1027 1031 1040 1043 -7.781132
## 47            1027 1033 1040 1044 -7.744992
## 48            1027 1034 1040 1043 -7.744316
## 49            1029 1035 1036 1042 -7.152003
## 50            1029 1032 1036 1045 -7.113658
## 51            1029 1035 1037 1041 -7.111188
## 52            1026 1035 1039 1042 -7.107568
## 53            1030 1032 1039 1041 -7.097960
## 54            1027 1035 1039 1041 -7.091016
## 55            1030 1031 1039 1042 -7.085682
## 56            1026 1032 1039 1045 -7.069452
## 57            1030 1034 1036 1042 -7.069254
## 58            1029 1032 1040 1041 -7.068363
## 59            1029 1031 1037 1045 -7.062114
## 60            1030 1032 1036 1044 -7.061722
## 61            1029 1031 1040 1042 -7.055832
## 62            1027 1035 1036 1044 -7.053333
## 63            1027 1031 1039 1045 -7.043125
## 64            1026 1035 1037 1044 -7.030250
## 65            1030 1034 1037 1041 -7.027609
## 66            1027 1034 1036 1045 -7.024986
## 67            1030 1031 1037 1044 -7.009450
## 68            1026 1034 1037 1045 -7.001977
## 69            1026 1034 1040 1042 -6.997288
## 70            1026 1032 1040 1044 -6.989097
## 71            1027 1034 1040 1041 -6.979952
## 72            1027 1031 1040 1044 -6.961929
## 73            1029 1033 1036 1042 -6.399282
## 74            1029 1031 1038 1042 -6.398130
## 75            1029 1032 1038 1041 -6.395106
## 76            1028 1031 1039 1042 -6.381290
## 77            1028 1032 1039 1041 -6.377761
## 78            1029 1032 1036 1043 -6.370396
## 79            1029 1033 1037 1041 -6.369336
## 80            1029 1031 1037 1043 -6.345000
## 81            1028 1034 1036 1042 -6.342272
## 82            1026 1033 1039 1042 -6.339745
## 83            1027 1033 1039 1041 -6.330802
## 84            1028 1032 1036 1044 -6.315192
## 85            1028 1034 1037 1041 -6.312793
## 86            1026 1032 1039 1043 -6.309469
## 87            1027 1031 1039 1043 -6.306180
## 88            1026 1034 1038 1042 -6.299689
## 89            1028 1031 1037 1044 -6.291242
## 90            1027 1034 1038 1041 -6.290642
## 91            1026 1032 1038 1044 -6.271700
## 92            1027 1031 1038 1044 -6.268827
## 93            1027 1033 1036 1044 -6.268725
## 94            1027 1034 1036 1043 -6.265904
## 95            1026 1033 1037 1044 -6.249541
## 96            1026 1034 1037 1043 -6.246754
## 97            1029 1033 1036 1045 -5.720024
## 98            1029 1035 1038 1041 -5.714463
## 99            1028 1035 1039 1041 -5.714243
## 100           1029 1035 1036 1043 -5.710035
## 101           1029 1031 1038 1045 -5.708712
## 102           1028 1031 1039 1045 -5.708588
## 103           1026 1033 1039 1045 -5.694937
## 104           1026 1035 1039 1043 -5.685026
## 105           1028 1035 1036 1044 -5.675590
## 106           1028 1034 1036 1045 -5.671573
## 107           1026 1035 1038 1044 -5.650312
## 108           1026 1034 1038 1045 -5.646338
## 109           1029 1033 1040 1041 -5.626516
## 110           1030 1033 1039 1041 -5.623941
## 111           1029 1031 1040 1043 -5.611557
## 112           1030 1031 1039 1043 -5.608923
## 113           1030 1033 1036 1044 -5.588388
## 114           1028 1034 1040 1041 -5.580897
## 115           1028 1031 1040 1044 -5.580204
## 116           1030 1034 1038 1041 -5.578031
## 117           1030 1031 1038 1044 -5.577377
## 118           1030 1034 1036 1043 -5.573941
## 119           1026 1033 1040 1044 -5.567516
## 120           1026 1034 1040 1043 -5.553379
MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected")

Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.

filtered_data = ds_metaecosystems %>%
                         filter(time_point >= first_time_point_model,
                                time_point <= last_time_point_model,
                                metaecosystem_type %in% metaecosystem_type_i)
plot.metaecos.points(filtered_data,
                     metaecosystem_type_i,
                     response_variable)

Then, given that we have gathered measurements from the same meta-ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this meta-ecosystem variable. To study the effects of connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat system nr as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | system nr)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | system nr)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | system nr)).

Unconnected meta-ecosystems are made of paired unconnected ecosystems, which are paired randomly. However, how to pair unconnected ecosystems can be done in multiple ways, as unconnected ecosystems did not interact and therefore any combination between ecosystems would be arbitrary. To make sure that the random combination we selected did not bias our results, we run all the possible combinations of ecosystems constituting unconnected meta-ecosystems. The ecosystem combinations are into the objects unconnected_combinations_sets (Data > Meta-ecosystems). We therefore compute a p-value for each unconnected ecosystems combination, creating a p-value distribution. We keep as p-value of the comparison the mean of such distributions.

Click to view the code we used to computed the p-values

 

If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.

unconnected_combinations_sets_filtered =  unconnected_combinations_sets %>%
  filter(disturbance == disturbance_global_input,
         metaecosystem_type %in% metaecosystem_type_i)

n_sets = unconnected_combinations_sets_filtered %>%
  pull(set) %>%
  max()

iterated_results_table = data.frame(Response = as.character(NA),
                                    Levels = as.character(NA),
                                    ΔAIC_full = NA,
                                    p_full = NA,
                                    ΔR2_full = NA,
                                    ΔAIC_fix = NA,
                                    p_fix = NA,
                                    ΔR2_fix = NA,
                                    combination_set = NA,
                                    system_nr_unconnected_systems = as.character(NA)) %>%
  slice(-1)

for (set_input in 1:n_sets) {
  
  system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           connection == "unconnected",
           set == set_input) %>%
    pull(system_nr)
  
  filtered_data = ds_metaecosystems %>%
    filter(time_point >= first_time_point_model,
           time_point <= last_time_point_model,
           metaecosystem_type %in% metaecosystem_type_i,
           connection == "connected" | 
           (connection == "unconnected" &
           system_nr %in% system_nr_unconnected_systems_input))
  
  null_model = lmer(
    get(response_variable) ~
      day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  full_model = lmer(
    get(response_variable) ~
      day +
      connection +
      connection:day +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_full = compute.model.stats(full_model,
                                         null_model,
                                         "mixed_model")
  
  reduced_model = lmer(
    get(response_variable) ~
      day +
      connection +
      (day | system_nr),
    data = filtered_data,
    REML = FALSE,
    control = lmerControl(optimizer = optimizer_input,
                          optCtrl = list(method = method_input)))
  
  model_stats_fixed = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model")
  
  iterated_results_table = fill.results.table(iterated_results_table,
                                              response_variable,
                                              metaecosystem_type_i,
                                              model_stats_full,
                                              model_stats_fixed)
  
  iterated_results_table$set[nrow(iterated_results_table)] = 
    set_input
  
  iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] = 
    paste(system_nr_unconnected_systems_input, collapse = " ")
}
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
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## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored

 
 
 

Full vs null model

Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
  deltaAIC = mean(iterated_results_table$ΔAIC_full),
  p_value = mean(iterated_results_table$p_full),
  R2 = NA
)

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.3   0.167     none
Click to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 

hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_full) %>%
  arrange(ΔAIC_full)
##    system_nr_unconnected_systems   ΔAIC_full
## 1                      1056 1065 -0.62042593
## 2                      1065 1056 -0.62042593
## 3                      1058 1062 -0.49794844
## 4                      1062 1058 -0.49794844
## 5                      1056 1064 -0.26493674
## 6                      1064 1056 -0.26493674
## 7                      1059 1061 -0.20354500
## 8                      1061 1059 -0.20354500
## 9                      1057 1062 -0.19138169
## 10                     1062 1057 -0.19138169
## 11                     1057 1065  0.02135567
## 12                     1065 1057  0.02135567
## 13                     1058 1064  0.05043751
## 14                     1064 1058  0.05043751
## 15                     1059 1060  0.10548001
## 16                     1060 1059  0.10548001
## 17                     1059 1063  0.34923867
## 18                     1063 1059  0.34923867
## 19                     1060 1065  0.74571276
## 20                     1065 1060  0.74571276
## 21                     1061 1064  0.76203591
## 22                     1064 1061  0.76203591
## 23                     1062 1063  0.84585905
## 24                     1063 1062  0.84585905
## 25                     1058 1060  1.20377042
## 26                     1060 1058  1.20377042
## 27                     1057 1061  1.22459781
## 28                     1061 1057  1.22459781
## 29                     1056 1063  1.24283225
## 30                     1063 1056  1.24283225

 
 
 

Reduced vs null model

Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
                               p_value = mean(iterated_results_table$p_fix),
                               R2 = NA)

model_stats_fixed %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.9   0.356     none
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 

hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 

Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>% 
  select(system_nr_unconnected_systems,
         ΔAIC_fix) %>%
  arrange(ΔAIC_fix)
##    system_nr_unconnected_systems   ΔAIC_fix
## 1                      1056 1065 -0.6946471
## 2                      1065 1056 -0.6946471
## 3                      1058 1062 -0.6033386
## 4                      1062 1058 -0.6033386
## 5                      1059 1061 -0.4184667
## 6                      1061 1059 -0.4184667
## 7                      1056 1064  0.8085298
## 8                      1064 1056  0.8085298
## 9                      1057 1062  1.0136835
## 10                     1062 1057  1.0136835
## 11                     1061 1064  1.1260933
## 12                     1064 1061  1.1260933
## 13                     1058 1064  1.1906671
## 14                     1064 1058  1.1906671
## 15                     1059 1060  1.2606299
## 16                     1060 1059  1.2606299
## 17                     1057 1065  1.3250017
## 18                     1065 1057  1.3250017
## 19                     1060 1065  1.3423113
## 20                     1065 1060  1.3423113
## 21                     1057 1061  1.4404786
## 22                     1061 1057  1.4404786
## 23                     1062 1063  1.4615803
## 24                     1063 1062  1.4615803
## 25                     1058 1060  1.5149510
## 26                     1060 1058  1.5149510
## 27                     1056 1063  1.5979996
## 28                     1063 1056  1.5979996
## 29                     1059 1063  1.6311258
## 30                     1063 1059  1.6311258

All ecosystems

ecosystem_type_i = c("Small unconnected",
                     "Medium unconnected",
                     "Large unconnected",
                     "Small connected to small",
                     "Small connected to large",
                     "Medium connected to medium",
                     "Large connected to small",
                     "Large connected to large")

BEF

ds_ecosystems %>%
    filter(is.na(species_richness) != TRUE) %>%
    ggplot(aes(x = species_richness,
               y = bioarea_mm2_per_ml)) +
    geom_point() +
    xlim(0, length(protist_species)) +
    labs(x = axis_names$axis_name[axis_names$variable == "species_richness"],
         y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

ds_ecosystems %>%
  filter(is.na(shannon) != TRUE) %>%
  ggplot(aes(x = shannon,
             y = bioarea_mm2_per_ml)) +
  geom_point() +
  labs(x = axis_names$axis_name[axis_names$variable == "shannon"],
       y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
  theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

ds_ecosystems %>%
  filter(is.na(evenness_pielou) != TRUE) %>%
  ggplot(aes(x = evenness_pielou,
             y = bioarea_mm2_per_ml)) +
  geom_point() +
  labs(x = axis_names$axis_name[axis_names$variable == "evenness_pielou"],
       y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
  theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

\(S\) vs \(M\) vs \(L\)

ecosystem_type_i = c("Small unconnected",
                 "Medium unconnected",
                 "Large unconnected")

Shannon

response_variable = "shannon"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))
## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+01


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1      -35 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     62.9     86.4    -21.4     42.9       68 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.37  -0.62   0.05   0.68   2.38 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-11    5e-06         
##             day         2e-14    1e-07    -1.00
##  Residual               1e-01    3e-01         
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                 1e+00      2e-01  8e+01     9.0    9e-14 ***
## ecosystem_sizeMedium       -3e-01      2e-01  8e+01    -1.2      0.2    
## ecosystem_sizeSmall         1e-01      3e-01  8e+01     0.5      0.6    
## day                        -7e-04      9e-03  8e+01    -0.1      0.9    
## ecosystem_sizeMedium:day    3e-03      1e-02  8e+01     0.3      0.8    
## ecosystem_sizeSmall:day    -7e-02      1e-02  8e+01    -4.8    6e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.622  0.440                     
## day         -0.935  0.661  0.582              
## ecsystm_sM:  0.661 -0.935 -0.411 -0.707       
## ecsystm_sS:  0.541 -0.382 -0.931 -0.578  0.409
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -20.2 < 0.001 **** very strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     77.7     96.5    -30.8     61.7       70 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -1.90  -0.62  -0.05   0.66   2.27 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-01    0.51          
##             day         8e-04    0.03     -1.00
##  Residual               1e-01    0.33          
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)             1.778      0.179 14.000      10    1e-07 ***
## ecosystem_sizeMedium   -0.220      0.084 62.158      -3     0.01 *  
## ecosystem_sizeSmall    -1.093      0.099 54.140     -11    2e-15 ***
## day                    -0.017      0.009 12.450      -2     0.09 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.235              
## ecsystm_szS -0.277  0.424       
## day         -0.943  0.000  0.082
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -33.7 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    202.4    226.7    -91.2    182.4       74 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.36  -0.72  -0.01   0.53   2.48 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.131         
##             day         5e-05    0.007    -1.00
##  Residual               5e-01    0.715         
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                  5.94       0.37 15.56    15.9    5e-11 ***
## ecosystem_sizeMedium        -1.63       0.53 15.56    -3.1    0.007 ** 
## ecosystem_sizeSmall         -4.14       0.56 15.56    -7.4    2e-06 ***
## day                         -0.16       0.02 14.38    -8.3    8e-07 ***
## ecosystem_sizeMedium:day     0.02       0.03 14.38     0.8    0.421    
## ecosystem_sizeSmall:day      0.08       0.03 14.38     2.9    0.011 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.667  0.471                     
## day         -0.937  0.662  0.624              
## ecsystm_sM:  0.662 -0.937 -0.442 -0.707       
## ecsystm_sS:  0.624 -0.442 -0.937 -0.667  0.471
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -30.8 < 0.001 **** very strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    205.3    224.7    -94.6    189.3       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.1   -0.8   -0.1    0.7    2.4 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 0.419    0.65          
##             day         0.001    0.04     -1.00
##  Residual               0.511    0.72          
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)              5.35       0.30 17.96      18    7e-13 ***
## ecosystem_sizeMedium    -1.22       0.18 69.16      -7    7e-09 ***
## ecosystem_sizeSmall     -2.60       0.20 69.16     -13   <2e-16 ***
## day                     -0.13       0.01 14.02      -9    6e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.309              
## ecsystm_szS -0.292  0.471       
## day         -0.899  0.000  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -37.8 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    306.0    330.3   -143.0    286.0       74 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.52  -0.60   0.04   0.74   2.12 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         1e-14    1e-07     NaN
##  Residual               2e+00    1e+00        
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                  7.17       0.68 84.00    10.5   <2e-16 ***
## ecosystem_sizeMedium         0.33       0.97 84.00     0.3     0.74    
## ecosystem_sizeSmall         -1.09       1.02 84.00    -1.1     0.29    
## day                         -0.02       0.04 84.00    -0.5     0.60    
## ecosystem_sizeMedium:day    -0.09       0.05 84.00    -1.8     0.08 .  
## ecosystem_sizeSmall:day     -0.22       0.05 84.00    -4.1    1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.667  0.471                     
## day         -0.935  0.661  0.623              
## ecsystm_sM:  0.661 -0.935 -0.441 -0.707       
## ecsystm_sS:  0.623 -0.441 -0.935 -0.667  0.471
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -28.7 < 0.001 **** very strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    315.1    334.6   -149.6    299.1       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.6   -0.1    0.5    2.4 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1.795    1.34          
##             day         0.005    0.07     -1.00
##  Residual               1.875    1.37          
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)              8.89       0.59 16.76      15    3e-11 ***
## ecosystem_sizeMedium    -1.30       0.35 66.58      -4    5e-04 ***
## ecosystem_sizeSmall     -5.08       0.38 66.58     -14   <2e-16 ***
## day                     -0.11       0.03 14.06      -4    0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.302              
## ecsystm_szS -0.284  0.471       
## day         -0.904  0.000  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -37.6 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -64.1    -41.1     42.1    -84.1       64 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.6   -0.6    0.2    0.5    3.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         1e-17    4e-09     NaN
##  Residual               2e-02    1e-01        
## Number of obs: 74, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                 8e-01      7e-02  7e+01    10.7   <2e-16 ***
## ecosystem_sizeMedium       -2e-01      1e-01  7e+01    -2.1     0.04 *  
## ecosystem_sizeSmall         5e-01      1e-01  7e+01     4.0    1e-04 ***
## day                         5e-04      4e-03  7e+01     0.1     0.88    
## ecosystem_sizeMedium:day    1e-02      5e-03  7e+01     2.2     0.03 *  
## ecosystem_sizeSmall:day    -5e-02      6e-03  7e+01    -7.5    1e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.623  0.441                     
## day         -0.935  0.661  0.583              
## ecsystm_sM:  0.661 -0.935 -0.412 -0.707       
## ecsystm_sS:  0.563 -0.398 -0.919 -0.602  0.426
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -11.5 < 0.001 **** very strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -38.1    -19.6     27.0    -54.1       66 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.2   -0.5    0.1    0.5    2.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-01    0.44          
##             day         6e-04    0.02     -1.00
##  Residual               2e-02    0.14          
## Number of obs: 74, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)             9e-01      1e-01  1e+01       7    8e-06 ***
## ecosystem_sizeMedium   -5e-04      4e-02  6e+01       0      1.0    
## ecosystem_sizeSmall    -4e-01      5e-02  5e+01      -9    1e-11 ***
## day                    -8e-03      7e-03  1e+01      -1      0.2    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.139              
## ecsystm_szS -0.142  0.389       
## day         -0.981  0.000  0.035
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.2   0.057   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1285.6   1309.2   -632.8   1265.6       68 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.85  -0.45   0.04   0.59   2.84 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e+05    310           
##             day         3e+01      6      -1.00
##  Residual               6e+05    782           
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                  3337        426    23     7.8    6e-08 ***
## ecosystem_sizeMedium          -21        602    23     0.0     0.97    
## ecosystem_sizeSmall         -1222        680    28    -1.8     0.08 .  
## day                            -7         21    44    -0.3     0.73    
## ecosystem_sizeMedium:day       31         30    44     1.1     0.30    
## ecosystem_sizeSmall:day        66         36    50     1.8     0.08 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.626  0.443                     
## day         -0.916  0.648  0.574              
## ecsystm_sM:  0.648 -0.916 -0.406 -0.707       
## ecsystm_sS:  0.531 -0.375 -0.913 -0.579  0.410
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1       -2    0.05   * weak
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1284.8   1303.7   -634.4   1268.8       70 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.98  -0.34   0.05   0.55   2.75 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e+05    434           
##             day         2e+02     14      -1.00
##  Residual               6e+05    800           
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)              2846        314   21     9.0    1e-08 ***
## ecosystem_sizeMedium      576        235   11     2.5     0.03 *  
## ecosystem_sizeSmall       -63        273   14    -0.2     0.82    
## day                        18         14   22     1.3     0.20    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.373              
## ecsystm_szS -0.419  0.429       
## day         -0.850  0.000  0.116
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Auto/Hetero

response_variable = "auto_hetero_ratio"

We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

save_results_in_table = TRUE

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(metaecosystem == "no",
         time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how ecosystem size influenced this variable. To study the effects of ecosystem size we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of size with time (Response variable ~ size * day + (day | culture ID)), the reduced model contains the size but without the interaction with time (Response variable ~ size + day + (day | culture ID)), and the null model doesn’t contain the size at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem size had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_size * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_size + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -3.1   0.026 ** moderate
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -2.3     21.3     11.2    -22.3       68 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.4   -0.1    0.3    6.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.14          
##             day         1e-04    0.01     -1.00
##  Residual               4e-02    0.20          
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                          Estimate Std. Error     df t value Pr(>|t|)   
## (Intercept)                -0.153      0.120 22.622      -1    0.215   
## ecosystem_sizeMedium        0.218      0.170 22.622       1    0.211   
## ecosystem_sizeSmall         0.317      0.189 26.479       2    0.106   
## day                         0.024      0.007 15.956       3    0.005 **
## ecosystem_sizeMedium:day   -0.022      0.010 15.956      -2    0.046 * 
## ecosystem_sizeSmall:day    -0.030      0.012 21.388      -3    0.017 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S day    ecs_M:
## ecsystm_szM -0.707                            
## ecsystm_szS -0.633  0.448                     
## day         -0.943  0.667  0.597              
## ecsystm_sM:  0.667 -0.943 -0.422 -0.707       
## ecsystm_sS:  0.579 -0.410 -0.944 -0.614  0.434
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.4   0.109     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##      0.3     19.2      7.8    -15.7       70 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.3   -0.1    0.3    6.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 5e-02    0.22          
##             day         3e-04    0.02     -1.00
##  Residual               4e-02    0.20          
## Number of obs: 78, groups:  culture_ID, 14
## 
## Fixed effects:
##                      Estimate Std. Error     df t value Pr(>|t|)  
## (Intercept)             0.091      0.093 23.009       1     0.34  
## ecosystem_sizeMedium   -0.122      0.056 42.120      -2     0.04 *
## ecosystem_sizeSmall    -0.146      0.062 50.826      -2     0.02 *
## day                     0.008      0.005 15.176       1     0.17  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.303              
## ecsystm_szS -0.312  0.452       
## day         -0.903  0.000  0.042
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Small unconnected"

## [1] "Medium unconnected"

## [1] "Large unconnected"

\(S_{L}\) vs \(S\)

ecosystem_type_i = c("Small connected to large",
                 "Small unconnected")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -5.4   0.009 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     62.7     77.6    -23.3     46.7       40 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.5    0.1    0.6    2.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 5e-04    0.023         
##             day         4e-05    0.006    -1.00
##  Residual               1e-01    0.382         
## Number of obs: 48, groups:  culture_ID, 9
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            2.017      0.197 38.690    10.2    1e-12
## ecosystem_typeSmall unconnected       -0.391      0.317 39.094    -1.2      0.2
## day                                   -0.065      0.011 24.167    -6.1    2e-06
## ecosystem_typeSmall unconnected:day   -0.007      0.018 30.372    -0.4      0.7
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.622              
## day         -0.913  0.568       
## ecsystm_Su:  0.533 -0.915 -0.584
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.2   0.002 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     60.8     73.9    -23.4     46.8       41 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.5    0.1    0.6    2.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 5e-04    0.023         
##             day         4e-05    0.006    -1.00
##  Residual               1e-01    0.383         
## Number of obs: 48, groups:  culture_ID, 9
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        2.058      0.167 43.391      12    9e-16 ***
## ecosystem_typeSmall unconnected   -0.504      0.128 14.192      -4    0.001 ** 
## day                               -0.068      0.009 27.070      -8    2e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.394       
## day         -0.876  0.103
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -3.9   0.019 ** moderate
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    113.7    129.6    -48.8     97.7       46 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.1   -0.6    0.0    0.5    3.3 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-11    5e-06         
##             day         1e-14    1e-07    -1.00
##  Residual               4e-01    6e-01         
## Number of obs: 54, groups:  culture_ID, 9
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             3.04       0.31 54.00      10    1e-13
## ecosystem_typeSmall unconnected        -1.24       0.46 54.00      -3    0.009
## day                                    -0.12       0.02 54.00      -8    7e-10
## ecosystem_typeSmall unconnected:day     0.04       0.02 54.00       2    0.068
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected     ** 
## day                                 ***
## ecosystem_typeSmall unconnected:day .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.667              
## day         -0.935  0.623       
## ecsystm_Su:  0.623 -0.935 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -2.6   0.032 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    115.0    128.9    -50.5    101.0       47 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -1.9   -0.7   -0.1    0.4    3.4 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e-02    0.24          
##             day         1e-04    0.01     -1.00
##  Residual               4e-01    0.61          
## Number of obs: 54, groups:  culture_ID, 9
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         2.68       0.26  9.52      10    2e-06 ***
## ecosystem_typeSmall unconnected    -0.43       0.17 44.23      -2     0.01 *  
## day                                -0.10       0.01 11.58      -8    6e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.290       
## day         -0.900  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.3   0.003 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    207.1    223.0    -95.6    191.1       46 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.06  -0.56   0.07   0.41   2.34 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         6e-15    8e-08     NaN
##  Residual               2e+00    1e+00        
## Number of obs: 54, groups:  culture_ID, 9
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             8.12       0.73 54.00    11.1    1e-15
## ecosystem_typeSmall unconnected        -2.04       1.10 54.00    -1.9     0.07
## day                                    -0.27       0.04 54.00    -7.0    4e-09
## ecosystem_typeSmall unconnected:day     0.03       0.06 54.00     0.5     0.60
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected     .  
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.667              
## day         -0.935  0.623       
## ecsystm_Su:  0.623 -0.935 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1       -9   0.001 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    205.4    219.3    -95.7    191.4       47 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.0   -0.6    0.1    0.5    2.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         2e-14    1e-07     NaN
##  Residual               2e+00    1e+00        
## Number of obs: 54, groups:  culture_ID, 9
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         7.88       0.57 54.00      14   <2e-16 ***
## ecosystem_typeSmall unconnected    -1.50       0.39 54.00      -4    3e-04 ***
## day                                -0.25       0.03 54.00      -9    4e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.302       
## day         -0.891  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -23.9 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -17.4     -4.5     16.7    -33.4       29 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.2   -0.5    0.0    0.4    2.7 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-03    0.047         
##             day         4e-06    0.002    -1.00
##  Residual               2e-02    0.153         
## Number of obs: 37, groups:  culture_ID, 9
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            0.820      0.089 10.000     9.2    3e-06
## ecosystem_typeSmall unconnected        0.393      0.135 10.380     2.9     0.01
## day                                    0.004      0.005 24.672     0.9     0.39
## ecosystem_typeSmall unconnected:day   -0.050      0.007 23.986    -6.6    7e-07
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected     *  
## day                                    
## ecosystem_typeSmall unconnected:day ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.660              
## day         -0.931  0.614       
## ecsystm_Su:  0.629 -0.920 -0.676
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -8.4   0.001 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -2.0      9.3      8.0    -16.0       30 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.77  -0.50  -0.06   0.48   2.39 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-01    0.46          
##             day         6e-04    0.02     -1.00
##  Residual               2e-02    0.16          
## Number of obs: 37, groups:  culture_ID, 9
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        1.236      0.168  7.497       7    1e-04 ***
## ecosystem_typeSmall unconnected   -0.537      0.057 22.910     -10    2e-09 ***
## day                               -0.018      0.009  8.949      -2     0.07 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.113       
## day         -0.977 -0.022
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))
## Warning: Model failed to converge with 1 negative eigenvalue: -1.3e-02
null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))
## Warning: Model failed to converge with 1 negative eigenvalue: -3.0e-02


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.7   0.512     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    827.3    842.3   -405.7    811.3       40 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.79  -0.38  -0.03   0.62   1.77 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 8e+03     87           
##             day         2e+03     49      -1.00
##  Residual               1e+06    982           
## Number of obs: 48, groups:  culture_ID, 9
## 
## Fixed effects:
##                                     Estimate Std. Error   df t value Pr(>|t|)
## (Intercept)                             2364        507   37     4.7    4e-05
## ecosystem_typeSmall unconnected         -325        815   38    -0.4     0.69
## day                                       83         34   11     2.5     0.03
## ecosystem_typeSmall unconnected:day      -20         56   15    -0.4     0.72
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 *  
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.621              
## day         -0.767  0.477       
## ecsystm_Su:  0.468 -0.797 -0.609
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.9   0.284     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    825.5    838.6   -405.8    811.5       41 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.79  -0.46  -0.03   0.58   1.78 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00      0          
##             day         2e+03     44       NaN
##  Residual               1e+06    983          
## Number of obs: 48, groups:  culture_ID, 9
## 
## Fixed effects:
##                                 Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)                         2451        451   40       5    3e-06 ***
## ecosystem_typeSmall unconnected     -561        511   11      -1     0.30    
## day                                   76         26   15       3     0.01 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.481       
## day         -0.665 -0.017
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Small connected to large"

## [1] "Small unconnected"

\(S_{L}\) vs \(S_{S}\)

ecosystem_type_i = c("Small connected to large",
                 "Small connected to small")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -2.2   0.045 ** moderate
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     74.2     93.7    -29.1     58.2       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -3.11  -0.47   0.01   0.68   2.55 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.15          
##             day         2e-04    0.01     -1.00
##  Residual               1e-01    0.32          
## Number of obs: 84, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error     df t value
## (Intercept)                                   2.017      0.179 28.034    11.2
## ecosystem_typeSmall connected to small       -0.177      0.224 29.392    -0.8
## day                                          -0.065      0.011 15.965    -6.0
## ecosystem_typeSmall connected to small:day   -0.004      0.014 17.612    -0.3
##                                            Pr(>|t|)    
## (Intercept)                                   7e-12 ***
## ecosystem_typeSmall connected to small          0.4    
## day                                           2e-05 ***
## ecosystem_typeSmall connected to small:day      0.8    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Scts day   
## ecsyst_Scts -0.800               
## day         -0.920  0.736        
## ecsys_Scts:  0.727 -0.923  -0.790
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -4.1   0.013 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     72.3     89.3    -29.2     58.3       77 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -3.09  -0.48   0.02   0.70   2.59 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.16          
##             day         2e-04    0.01     -1.00
##  Residual               1e-01    0.32          
## Number of obs: 84, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error     df t value
## (Intercept)                               2.051      0.123 52.993      17
## ecosystem_typeSmall connected to small   -0.231      0.086 26.679      -3
## day                                      -0.067      0.007 18.757     -10
##                                        Pr(>|t|)    
## (Intercept)                              <2e-16 ***
## ecosystem_typeSmall connected to small     0.01 *  
## day                                       4e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Scts
## ecsyst_Scts -0.486       
## day         -0.822  0.028
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.6    0.06   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    158.7    178.7    -71.4    142.7       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.6    0.0    0.5    3.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 5e-02    0.23          
##             day         9e-05    0.01     -1.00
##  Residual               3e-01    0.53          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error    df t value
## (Intercept)                                    3.04       0.29 16.95      10
## ecosystem_typeSmall connected to small        -0.82       0.36 16.95      -2
## day                                           -0.12       0.01 28.24      -8
## ecosystem_typeSmall connected to small:day     0.03       0.02 28.24       2
##                                            Pr(>|t|)    
## (Intercept)                                   8e-09 ***
## ecosystem_typeSmall connected to small         0.03 *  
## day                                           8e-09 ***
## ecosystem_typeSmall connected to small:day     0.09 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Scts day   
## ecsyst_Scts -0.816               
## day         -0.940  0.768        
## ecsys_Scts:  0.768 -0.940  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.6   0.104     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    159.7    177.2    -72.8    145.7       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.2   -0.7    0.0    0.5    3.7 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-01    0.34          
##             day         2e-04    0.02     -1.00
##  Residual               3e-01    0.53          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error     df t value
## (Intercept)                               2.637      0.198 19.628      13
## ecosystem_typeSmall connected to small   -0.218      0.123 54.872      -2
## day                                      -0.098      0.009 20.642     -11
##                                        Pr(>|t|)    
## (Intercept)                               3e-11 ***
## ecosystem_typeSmall connected to small     0.08 .  
## day                                       6e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Scts
## ecsyst_Scts -0.414       
## day         -0.862  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.6   0.003 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    294.1    314.1   -139.0    278.1       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.58  -0.65   0.01   0.43   2.93 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         4e-13    6e-07     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error    df t value
## (Intercept)                                    8.12       0.58 90.00      14
## ecosystem_typeSmall connected to small        -1.93       0.71 90.00      -3
## day                                           -0.27       0.03 90.00      -9
## ecosystem_typeSmall connected to small:day     0.06       0.04 90.00       2
##                                            Pr(>|t|)    
## (Intercept)                                  <2e-16 ***
## ecosystem_typeSmall connected to small        0.008 ** 
## day                                           1e-13 ***
## ecosystem_typeSmall connected to small:day    0.132    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Scts day   
## ecsyst_Scts -0.816               
## day         -0.935  0.763        
## ecsys_Scts:  0.763 -0.935  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.3   0.002 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    294.3    311.8   -140.2    280.3       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.43  -0.74   0.03   0.26   2.95 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         6e-14    3e-07     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error    df t value
## (Intercept)                                7.44       0.38 90.00      20
## ecosystem_typeSmall connected to small    -0.92       0.26 90.00      -4
## day                                       -0.23       0.02 90.00     -13
##                                        Pr(>|t|)    
## (Intercept)                              <2e-16 ***
## ecosystem_typeSmall connected to small    6e-04 ***
## day                                      <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Scts
## ecsyst_Scts -0.448       
## day         -0.836  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.1   0.004 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -15.9      1.8     15.9    -31.9       59 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -3.13  -0.61   0.03   0.52   2.23 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.118         
##             day         9e-05    0.009    -1.00
##  Residual               3e-02    0.180         
## Number of obs: 67, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error     df t value
## (Intercept)                                   0.821      0.117 27.360     7.0
## ecosystem_typeSmall connected to small        0.383      0.142 26.723     2.7
## day                                           0.004      0.007 16.874     0.6
## ecosystem_typeSmall connected to small:day   -0.034      0.009 16.314    -3.7
##                                            Pr(>|t|)    
## (Intercept)                                   1e-07 ***
## ecosystem_typeSmall connected to small        0.012 *  
## day                                           0.567    
## ecosystem_typeSmall connected to small:day    0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Scts day   
## ecsyst_Scts -0.823               
## day         -0.940  0.773        
## ecsys_Scts:  0.775 -0.938  -0.824
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.3   0.187     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     -8.6      6.9     11.3    -22.6       60 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.4   -0.6    0.0    0.5    1.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e-02    0.23          
##             day         3e-04    0.02     -1.00
##  Residual               3e-02    0.18          
## Number of obs: 67, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error     df t value
## (Intercept)                               1.125      0.092 23.749      12
## ecosystem_typeSmall connected to small   -0.084      0.051 45.033      -2
## day                                      -0.018      0.006 15.210      -3
##                                        Pr(>|t|)    
## (Intercept)                               1e-11 ***
## ecosystem_typeSmall connected to small     0.11    
## day                                        0.01 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Scts
## ecsyst_Scts -0.363       
## day         -0.895  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.4   0.068   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1445.3   1464.8   -714.7   1429.3       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.4    0.1    0.6    1.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 7e+04     272          
##             day         1e+03      39     -1.00
##  Residual               1e+06    1129          
## Number of obs: 84, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error   df t value
## (Intercept)                                    2364        593   50       4
## ecosystem_typeSmall connected to small          958        745   51       1
## day                                              83         35   21       2
## ecosystem_typeSmall connected to small:day      -94         44   23      -2
##                                            Pr(>|t|)    
## (Intercept)                                   2e-04 ***
## ecosystem_typeSmall connected to small         0.20    
## day                                            0.03 *  
## ecosystem_typeSmall connected to small:day     0.04 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Scts day   
## ecsyst_Scts -0.797               
## day         -0.896  0.714        
## ecsys_Scts:  0.702 -0.900  -0.784
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.7   0.246     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1447.4   1464.4   -716.7   1433.4       77 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.5    0.1    0.6    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e+05     525          
##             day         3e+03      54     -1.00
##  Residual               1e+06    1142          
## Number of obs: 84, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error   df t value
## (Intercept)                                3222        441   58       7
## ecosystem_typeSmall connected to small     -421        321   25      -1
## day                                          25         24   18       1
##                                        Pr(>|t|)    
## (Intercept)                               9e-10 ***
## ecosystem_typeSmall connected to small      0.2    
## day                                         0.3    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Scts
## ecsyst_Scts -0.502       
## day         -0.805  0.024
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Small connected to large"

## [1] "Small connected to small"

\(S_{S}\) vs \(S\)

ecosystem_type_i = c("Small connected to small",
                 "Small unconnected")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -2.4    0.04 ** moderate
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     62.3     80.5    -23.2     46.3       64 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.1   -0.5    0.0    0.7    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.12          
##             day         1e-04    0.01     -1.00
##  Residual               1e-01    0.32          
## Number of obs: 72, groups:  culture_ID, 14
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            1.834      0.130 25.655    14.1    1e-13
## ecosystem_typeSmall unconnected       -0.203      0.253 28.212    -0.8      0.4
## day                                   -0.068      0.008 16.552    -8.7    1e-07
## ecosystem_typeSmall unconnected:day   -0.004      0.016 20.778    -0.3      0.8
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.516              
## day         -0.928  0.479       
## ecsystm_Su:  0.469 -0.927 -0.505
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -4.4   0.012 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     60.4     76.3    -23.2     46.4       65 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.1   -0.5    0.0    0.7    2.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.13          
##             day         1e-04    0.01     -1.00
##  Residual               1e-01    0.32          
## Number of obs: 72, groups:  culture_ID, 14
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        1.851      0.115 30.052      16    3e-16 ***
## ecosystem_typeSmall unconnected   -0.267      0.095 23.137      -3     0.01 ** 
## day                               -0.069      0.007 17.719     -10    8e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.247       
## day         -0.907  0.033
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.1   0.142     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    111.5    130.9    -47.7     95.5       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.7    0.0    0.6    4.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 8e-03    0.087         
##             day         1e-05    0.004    -1.00
##  Residual               2e-01    0.426         
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            2.218      0.157 16.456    14.1    1e-10
## ecosystem_typeSmall unconnected       -0.421      0.295 16.456    -1.4      0.2
## day                                   -0.087      0.008 31.270   -10.7    5e-12
## ecosystem_typeSmall unconnected:day    0.012      0.015 31.270     0.8      0.4
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.535              
## day         -0.936  0.500       
## ecsystm_Su:  0.500 -0.936 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.3   0.071   * weak
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    110.1    127.2    -48.1     96.1       77 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.3   -0.7   -0.1    0.6    4.3 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.119         
##             day         3e-05    0.005    -1.00
##  Residual               2e-01    0.427         
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        2.153      0.138 16.579      16    3e-11 ***
## ecosystem_typeSmall unconnected   -0.196      0.104 60.171      -2     0.06 .  
## day                               -0.084      0.007 27.861     -12    1e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.215       
## day         -0.915  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.4   0.069   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    266.5    286.0   -125.3    250.5       76 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.7   -0.1    0.5    2.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         7e-14    3e-07     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             6.18       0.39 84.00    15.8   <2e-16
## ecosystem_typeSmall unconnected        -0.11       0.73 84.00    -0.1      0.9
## day                                    -0.21       0.02 84.00   -10.3   <2e-16
## ecosystem_typeSmall unconnected:day    -0.03       0.04 84.00    -0.7      0.5
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.535              
## day         -0.935  0.500       
## ecsystm_Su:  0.500 -0.935 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -2.9   0.027 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    265.0    282.0   -125.5    251.0       77 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.7   -0.1    0.4    2.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         7e-15    8e-08     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 84, groups:  culture_ID, 14
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         6.32       0.34 84.00      19   <2e-16 ***
## ecosystem_typeSmall unconnected    -0.58       0.26 84.00      -2     0.03 *  
## day                                -0.22       0.02 84.00     -13   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.219       
## day         -0.912  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))
## Warning: Model failed to converge with 1 negative eigenvalue: -1.9e+00


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1       -8   0.003 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     11.4     27.9      2.3     -4.6       50 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.36  -0.58   0.04   0.78   1.96 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 9e-03    0.095         
##             day         5e-05    0.007    -1.00
##  Residual               5e-02    0.227         
## Number of obs: 58, groups:  culture_ID, 14
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            1.210      0.094 28.012      13    3e-13
## ecosystem_typeSmall unconnected        0.008      0.180 31.856       0      1.0
## day                                   -0.030      0.006 15.767      -5    7e-05
## ecosystem_typeSmall unconnected:day   -0.016      0.010 18.860      -2      0.1
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                 ***
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.521              
## day         -0.928  0.483       
## ecsystm_Su:  0.497 -0.920 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.8   0.002 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     11.6     26.0      1.2     -2.4       51 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.3   -0.7   -0.1    0.8    2.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.122         
##             day         8e-05    0.009    -1.00
##  Residual               5e-02    0.229         
## Number of obs: 58, groups:  culture_ID, 14
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        1.280      0.085 26.147      15    2e-14 ***
## ecosystem_typeSmall unconnected   -0.240      0.072 44.623      -3    0.002 ** 
## day                               -0.034      0.005 15.417      -7    5e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.179       
## day         -0.909 -0.030
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.9    0.35     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1233.5   1251.7   -608.8   1217.5       64 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.5    0.2    0.6    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-03    4e-02         
##             day         2e-06    1e-03    -1.00
##  Residual               1e+06    1e+03         
## Number of obs: 72, groups:  culture_ID, 14
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             3335        439    72     7.6    9e-11
## ecosystem_typeSmall unconnected        -1226        857    72    -1.4      0.2
## day                                      -12         24    72    -0.5      0.6
## ecosystem_typeSmall unconnected:day       71         49    72     1.4      0.2
##                                        
## (Intercept)                         ***
## ecosystem_typeSmall unconnected        
## day                                    
## ecosystem_typeSmall unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su day   
## ecsystm_tSu -0.512              
## day         -0.936  0.479       
## ecsystm_Su:  0.460 -0.932 -0.492
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.9   0.806     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1233.5   1249.5   -609.8   1219.5       65 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.5    0.2    0.7    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 7e-04    3e-02         
##             day         2e-06    1e-03    -1.00
##  Residual               1e+06    1e+03         
## Number of obs: 72, groups:  culture_ID, 14
## 
## Fixed effects:
##                                 Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)                         3044        395   72     7.7    5e-11 ***
## ecosystem_typeSmall unconnected      -77        314   72    -0.2      0.8    
## day                                    5         21   72     0.3      0.8    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Su
## ecsystm_tSu -0.258       
## day         -0.918  0.065
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Small connected to small"

## [1] "Small unconnected"

\(L_{S}\) vs \(L\)

ecosystem_type_i = c("Large connected to small",
                 "Large unconnected")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1        1    0.22     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     34.0     50.7     -9.0     18.0       52 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.93  -0.65  -0.06   0.77   1.72 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.125         
##             day         6e-05    0.008    -1.00
##  Residual               8e-02    0.276         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            1.224      0.153 16.644     8.0    4e-07
## ecosystem_typeLarge unconnected        0.257      0.216 16.644     1.2      0.3
## day                                    0.007      0.008 11.109     0.9      0.4
## ecosystem_typeLarge unconnected:day   -0.008      0.012 11.109    -0.7      0.5
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                    
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.707              
## day         -0.943  0.667       
## ecsystm_Lu:  0.667 -0.943 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.6   0.109     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     32.5     47.1     -9.2     18.5       53 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.8   -0.7   -0.1    0.8    1.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-02    0.139         
##             day         8e-05    0.009    -1.00
##  Residual               8e-02    0.276         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                        1e+00      1e-01 2e+01    11.2    9e-10 ***
## ecosystem_typeLarge unconnected    1e-01      7e-02 5e+01     1.6      0.1    
## day                                3e-03      6e-03 1e+01     0.6      0.6    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.312       
## day         -0.898  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = 'optimx', 
                      optCtrl = list(method = 'nlminb')))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.5   0.003 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    168.5    185.3    -76.3    152.5       52 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -1.95  -0.70  -0.07   0.69   2.18 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 0.964    0.98          
##             day         0.002    0.05     -1.00
##  Residual               0.656    0.81          
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             4.76       0.61 10.04     7.9    1e-05
## ecosystem_typeLarge unconnected         1.18       0.86 10.04     1.4      0.2
## day                                    -0.15       0.03 10.62    -5.0    5e-04
## ecosystem_typeLarge unconnected:day    -0.01       0.04 10.62    -0.3      0.8
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                 ***
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.707              
## day         -0.965  0.683       
## ecsystm_Lu:  0.683 -0.965 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -9.5   0.001 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    166.6    181.3    -76.3    152.6       53 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -1.91  -0.69  -0.07   0.70   2.17 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 0.979    0.99          
##             day         0.002    0.05     -1.00
##  Residual               0.656    0.81          
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         4.88       0.44 11.29      11    2e-07 ***
## ecosystem_typeLarge unconnected     0.93       0.22 29.77       4    2e-04 ***
## day                                -0.15       0.02 10.60      -7    2e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.251       
## day         -0.935  0.000
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -5.6   0.008 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    198.3    215.1    -91.2    182.3       52 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.39  -0.72   0.05   0.89   2.13 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 8e-12    3e-06         
##             day         1e-14    1e-07    -1.00
##  Residual               1e+00    1e+00         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            6e+00      6e-01  6e+01    10.8    9e-16
## ecosystem_typeLarge unconnected        1e+00      8e-01  6e+01     1.2      0.2
## day                                   -2e-02      3e-02  6e+01    -0.6      0.5
## ecosystem_typeLarge unconnected:day   -6e-16      4e-02  6e+01     0.0      1.0
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                    
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.707              
## day         -0.935  0.661       
## ecsystm_Lu:  0.661 -0.935 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.6   0.002 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    196.3    211.0    -91.2    182.3       53 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.39  -0.72   0.05   0.89   2.13 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 8e-12    3e-06         
##             day         1e-14    1e-07    -1.00
##  Residual               1e+00    1e+00         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         6.17       0.43 60.00    14.4   <2e-16 ***
## ecosystem_typeLarge unconnected     1.00       0.29 60.00     3.5    9e-04 ***
## day                                -0.02       0.02 60.00    -0.9      0.4    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.334       
## day         -0.881  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.9   0.581     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -71.4    -54.7     43.7    -87.4       52 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.6    0.3    0.7    1.5 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-03    0.050         
##             day         1e-05    0.003    -1.00
##  Residual               1e-02    0.115         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            0.673      0.063 18.728    10.7    2e-09
## ecosystem_typeLarge unconnected        0.084      0.089 18.728     0.9      0.4
## day                                    0.006      0.003 11.621     1.7      0.1
## ecosystem_typeLarge unconnected:day   -0.005      0.005 11.621    -1.1      0.3
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                    
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.707              
## day         -0.942  0.666       
## ecsystm_Lu:  0.666 -0.942 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1        2   0.893     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    -72.4    -57.7     43.2    -86.4       53 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.6    0.2    0.8    1.5 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 4e-03    0.063         
##             day         2e-05    0.004    -1.00
##  Residual               1e-02    0.115         
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        0.717      0.049 19.377    14.7    5e-12 ***
## ecosystem_typeLarge unconnected   -0.004      0.030 44.928    -0.1      0.9    
## day                                0.003      0.003 10.997     1.2      0.2    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.309       
## day         -0.900  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.5   0.291     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    971.3    988.0   -477.6    955.3       52 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.6   -0.1    0.5    2.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e+04    170           
##             day         1e+02     12      -1.00
##  Residual               5e+05    688           
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                           3627.2      362.0   29.3    10.0    6e-11
## ecosystem_typeLarge unconnected       -290.4      511.9   29.3    -0.6      0.6
## day                                     -7.6       19.1   14.3    -0.4      0.7
## ecosystem_typeLarge unconnected:day      0.3       27.0   14.3     0.0      1.0
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                    
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.707              
## day         -0.937  0.662       
## ecsystm_Lu:  0.662 -0.937 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.5   0.116     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    969.3    983.9   -477.6    955.3       53 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.6   -0.1    0.5    2.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e+04    170           
##             day         1e+02     12      -1.00
##  Residual               5e+05    688           
## Number of obs: 60, groups:  culture_ID, 10
## 
## Fixed effects:
##                                 Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)                         3625        271   34    13.4    6e-15 ***
## ecosystem_typeLarge unconnected     -286        179   48    -1.6      0.1    
## day                                   -7         14   14    -0.5      0.6    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.331       
## day         -0.884  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Large connected to small"

## [1] "Large unconnected"

\(L_{S}\) vs \(L_{L}\)

ecosystem_type_i = c("Large connected to small",
                 "Large connected to large")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.4   0.271     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     35.2     55.2     -9.6     19.2       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -3.15  -0.67  -0.04   0.76   2.58 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.100         
##             day         3e-05    0.005    -1.00
##  Residual               7e-02    0.267         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error     df t value
## (Intercept)                                   1.224      0.144 15.394     8.5
## ecosystem_typeLarge connected to large        0.192      0.177 15.394     1.1
## day                                           0.007      0.007 16.266     1.0
## ecosystem_typeLarge connected to large:day   -0.006      0.009 16.266    -0.6
##                                            Pr(>|t|)    
## (Intercept)                                   3e-07 ***
## ecosystem_typeLarge connected to large          0.3    
## day                                             0.3    
## ecosystem_typeLarge connected to large:day      0.6    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Lctl day   
## ecsyst_Lctl -0.816               
## day         -0.941  0.768        
## ecsys_Lctl:  0.768 -0.941  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.2   0.134     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     33.5     51.0     -9.8     19.5       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -3.02  -0.72  -0.09   0.77   2.59 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.111         
##             day         3e-05    0.006    -1.00
##  Residual               7e-02    0.267         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error    df t value
## (Intercept)                               1e+00      9e-02 2e+01    13.8
## ecosystem_typeLarge connected to large    9e-02      6e-02 7e+01     1.5
## day                                       4e-03      4e-03 2e+01     0.8
##                                        Pr(>|t|)    
## (Intercept)                               2e-12 ***
## ecosystem_typeLarge connected to large      0.1    
## day                                         0.4    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Lctl
## ecsyst_Lctl -0.428       
## day         -0.852  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = 'optimx', 
                      optCtrl = list(method = 'nlminb')))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.9   0.085   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    254.5    274.5   -119.3    238.5       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.35  -0.53  -0.07   0.52   3.04 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 4e-01    0.61          
##             day         2e-04    0.02     -1.00
##  Residual               7e-01    0.86          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error    df t value
## (Intercept)                                    4.76       0.52 17.88     9.2
## ecosystem_typeLarge connected to large         1.03       0.64 17.88     1.6
## day                                           -0.15       0.02 33.39    -6.1
## ecosystem_typeLarge connected to large:day    -0.02       0.03 33.39    -0.7
##                                            Pr(>|t|)    
## (Intercept)                                   4e-08 ***
## ecosystem_typeLarge connected to large          0.1    
## day                                           6e-07 ***
## ecosystem_typeLarge connected to large:day      0.5    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Lctl day   
## ecsyst_Lctl -0.816               
## day         -0.914  0.747        
## ecsys_Lctl:  0.747 -0.914  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1     -2.4   0.036 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb"))
## 
##      AIC      BIC   logLik deviance df.resid 
##    253.1    270.6   -119.5    239.1       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.26  -0.57  -0.06   0.56   3.02 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 4e-01    0.63          
##             day         3e-04    0.02     -0.98
##  Residual               7e-01    0.86          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error    df t value
## (Intercept)                                5.05       0.35 21.50      14
## ecosystem_typeLarge connected to large     0.59       0.26 15.00       2
## day                                       -0.16       0.01 15.00     -12
##                                        Pr(>|t|)    
## (Intercept)                               1e-12 ***
## ecosystem_typeLarge connected to large     0.04 *  
## day                                       8e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Lctl
## ecsyst_Lctl -0.492       
## day         -0.798  0.000
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.1   0.078   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    298.4    318.4   -141.2    282.4       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.27  -0.69   0.04   0.87   2.17 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-02    0.18          
##             day         9e-05    0.01     -1.00
##  Residual               1e+00    1.16          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error    df t value
## (Intercept)                                    6.17       0.60 16.52    10.2
## ecosystem_typeLarge connected to large         1.28       0.74 16.52     1.7
## day                                           -0.02       0.03 15.54    -0.6
## ecosystem_typeLarge connected to large:day    -0.04       0.04 15.54    -1.1
##                                            Pr(>|t|)    
## (Intercept)                                   1e-08 ***
## ecosystem_typeLarge connected to large          0.1    
## day                                             0.6    
## ecosystem_typeLarge connected to large:day      0.3    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Lctl day   
## ecsyst_Lctl -0.816               
## day         -0.936  0.764        
## ecsys_Lctl:  0.764 -0.936  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value    evidence
## 1       -2   0.046 ** moderate
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    297.6    315.1   -141.8    283.6       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.02  -0.71   0.05   0.82   2.22 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-01    0.41          
##             day         5e-04    0.02     -1.00
##  Residual               1e+00    1.16          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error    df t value
## (Intercept)                                6.67       0.40 24.11      17
## ecosystem_typeLarge connected to large     0.53       0.26 75.30       2
## day                                       -0.05       0.02 15.32      -2
##                                        Pr(>|t|)    
## (Intercept)                               1e-14 ***
## ecosystem_typeLarge connected to large     0.04 *  
## day                                        0.03 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Lctl
## ecsyst_Lctl -0.433       
## day         -0.848  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      3.6   0.804     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -122.1   -102.1     69.1   -138.1       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.7   -0.6    0.1    0.8    1.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         3e-17    5e-09     NaN
##  Residual               1e-02    1e-01        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error     df t value
## (Intercept)                                   7e-01      6e-02  9e+01    11.6
## ecosystem_typeLarge connected to large        2e-02      7e-02  9e+01     0.3
## day                                           6e-03      3e-03  9e+01     1.9
## ecosystem_typeLarge connected to large:day   -3e-04      4e-03  9e+01    -0.1
##                                            Pr(>|t|)    
## (Intercept)                                  <2e-16 ***
## ecosystem_typeLarge connected to large         0.76    
## day                                            0.07 .  
## ecosystem_typeLarge connected to large:day     0.94    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Lctl day   
## ecsyst_Lctl -0.816               
## day         -0.935  0.763        
## ecsys_Lctl:  0.763 -0.935  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.6   0.512     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -124.1   -106.6     69.0   -138.1       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.7   -0.6    0.1    0.8    1.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         3e-17    5e-09     NaN
##  Residual               1e-02    1e-01        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error    df t value
## (Intercept)                               7e-01      4e-02 9e+01    18.1
## ecosystem_typeLarge connected to large    2e-02      3e-02 9e+01     0.7
## day                                       5e-03      2e-03 9e+01     3.1
##                                        Pr(>|t|)    
## (Intercept)                              <2e-16 ***
## ecosystem_typeLarge connected to large    0.513    
## day                                       0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Lctl
## ecsyst_Lctl -0.448       
## day         -0.836  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1     -7.5   0.003 *** strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1408.9   1428.9   -696.5   1392.9       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.2   -0.5   -0.1    0.5    3.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-04    1e-02         
##             day         5e-07    7e-04    -1.00
##  Residual               3e+05    6e+02         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                            Estimate Std. Error   df t value
## (Intercept)                                    3627        286   90    12.7
## ecosystem_typeLarge connected to large         -735        350   90    -2.1
## day                                              -8         15   90    -0.5
## ecosystem_typeLarge connected to large:day       56         18   90     3.1
##                                            Pr(>|t|)    
## (Intercept)                                  <2e-16 ***
## ecosystem_typeLarge connected to large        0.038 *  
## day                                           0.612    
## ecosystem_typeLarge connected to large:day    0.003 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ec_Lctl day   
## ecsyst_Lctl -0.816               
## day         -0.935  0.763        
## ecsys_Lctl:  0.763 -0.935  -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.9   0.087   * weak
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1415.4   1432.9   -700.7   1401.4       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.6    0.0    0.4    3.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 8e+04    291           
##             day         3e+02     17      -1.00
##  Residual               3e+05    571           
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                        Estimate Std. Error   df t value
## (Intercept)                                2969        204   29      14
## ecosystem_typeLarge connected to large      252        128   73       2
## day                                          30         10   15       3
##                                        Pr(>|t|)    
## (Intercept)                               9e-15 ***
## ecosystem_typeLarge connected to large    0.053 .  
## day                                       0.009 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) e_Lctl
## ecsyst_Lctl -0.418       
## day         -0.859  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Large connected to small"

## [1] "Large connected to large"

\(L_{L}\) vs \(L\)

ecosystem_type_i = c("Large connected to large",
                 "Large unconnected")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      3.8   0.887     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     21.2     41.2     -2.6      5.2       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.11  -0.72  -0.01   0.76   2.81 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.119         
##             day         5e-05    0.007    -1.00
##  Residual               6e-02    0.245         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            1.416      0.097 18.467    14.6    1e-11
## ecosystem_typeLarge unconnected        0.065      0.168 18.467     0.4      0.7
## day                                    0.002      0.005 15.168     0.3      0.7
## ecosystem_typeLarge unconnected:day   -0.002      0.009 15.168    -0.3      0.8
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                    
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.577              
## day         -0.945  0.546       
## ecsystm_Lu:  0.546 -0.945 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.8   0.682     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     19.3     36.8     -2.7      5.3       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.13  -0.75   0.01   0.76   2.80 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-02    0.120         
##             day         5e-05    0.007    -1.00
##  Residual               6e-02    0.245         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                        1e+00      8e-02 2e+01    17.6    9e-14 ***
## ecosystem_typeLarge unconnected    2e-02      5e-02 7e+01     0.4      0.7    
## day                                9e-04      4e-03 2e+01     0.2      0.8    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.225       
## day         -0.921  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.1   0.396     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    265.4    285.4   -124.7    249.4       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -1.9   -0.6   -0.1    0.5    2.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e-02    0.248         
##             day         1e-05    0.003    -1.00
##  Residual               9e-01    0.950         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             5.79       0.35 31.23    16.3   <2e-16
## ecosystem_typeLarge unconnected         0.15       0.61 31.23     0.2      0.8
## day                                    -0.17       0.02 68.52    -9.4    6e-14
## ecosystem_typeLarge unconnected:day     0.01       0.03 68.52     0.3      0.8
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                 ***
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.577              
## day         -0.923  0.533       
## ecsystm_Lu:  0.533 -0.923 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.2   0.185     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    263.5    281.0   -124.8    249.5       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -1.9   -0.6   -0.1    0.5    2.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e-02    0.249         
##             day         1e-05    0.003    -1.00
##  Residual               9e-01    0.950         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         5.73       0.30 33.41      19   <2e-16 ***
## ecosystem_typeLarge unconnected     0.32       0.24 15.08       1      0.2    
## day                                -0.17       0.01 68.06     -11   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.263       
## day         -0.890  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -0.6   0.098   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    290.7    310.7   -137.4    274.7       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.02  -0.72   0.01   0.89   2.26 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         6e-13    8e-07     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                     Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                             7.45       0.41 90.00    18.4   <2e-16
## ecosystem_typeLarge unconnected        -0.28       0.70 90.00    -0.4    0.692
## day                                    -0.06       0.02 90.00    -2.9    0.005
## ecosystem_typeLarge unconnected:day     0.04       0.04 90.00     1.1    0.259
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                 ** 
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.577              
## day         -0.935  0.540       
## ecsystm_Lu:  0.540 -0.935 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.4   0.067   * weak
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    290.0    307.5   -138.0    276.0       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.05  -0.74  -0.09   0.77   2.27 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         2e-14    2e-07     NaN
##  Residual               1e+00    1e+00        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                 Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                         7.20       0.34 90.00      21   <2e-16 ***
## ecosystem_typeLarge unconnected     0.47       0.25 90.00       2    0.066 .  
## day                                -0.05       0.02 90.00      -3    0.009 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.243       
## day         -0.907  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.3   0.255     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -136.1   -116.1     76.0   -152.1       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.7    0.1    0.8    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-04    1e-02         
##             day         8e-07    9e-04    -1.00
##  Residual               1e-02    1e-01         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                     Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                            0.695      0.038 34.956      18   <2e-16
## ecosystem_typeLarge unconnected        0.063      0.066 34.956       1     0.35
## day                                    0.005      0.002 17.958       3     0.02
## ecosystem_typeLarge unconnected:day   -0.005      0.003 17.958      -1     0.18
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                 *  
## ecosystem_typeLarge unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.577              
## day         -0.936  0.540       
## ecsystm_Lu:  0.540 -0.936 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.1   0.345     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -136.2   -118.7     75.1   -150.2       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.5   -0.6    0.1    0.8    1.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-03    0.037         
##             day         5e-06    0.002    -1.00
##  Residual               1e-02    0.104         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                 Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                        0.723      0.033 28.478      22   <2e-16 ***
## ecosystem_typeLarge unconnected   -0.023      0.023 73.905      -1     0.34    
## day                                0.004      0.002 16.350       2     0.04 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.234       
## day         -0.914  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value         evidence
## 1    -13.9 < 0.001 **** very strong
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1416.8   1436.8   -700.4   1400.8       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.68  -0.56  -0.07   0.56   2.36 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 7e+04    256           
##             day         3e+02     16      -1.00
##  Residual               3e+05    569           
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                     Estimate Std. Error   df t value Pr(>|t|)
## (Intercept)                             2892        222   23      13    4e-12
## ecosystem_typeLarge unconnected          445        385   23       1     0.26
## day                                       48         12   16       4    9e-04
## ecosystem_typeLarge unconnected:day      -55         21   16      -3     0.02
##                                        
## (Intercept)                         ***
## ecosystem_typeLarge unconnected        
## day                                 ***
## ecosystem_typeLarge unconnected:day *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu day   
## ecsystm_tLu -0.577              
## day         -0.943  0.544       
## ecsystm_Lu:  0.544 -0.943 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value   evidence
## 1      -10   0.001 *** strong
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1420.7   1438.2   -703.3   1406.7       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.68  -0.54  -0.05   0.59   2.39 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e+05    503           
##             day         9e+02     30      -1.00
##  Residual               3e+05    570           
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                 Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)                         3212        218   18      15    2e-11 ***
## ecosystem_typeLarge unconnected     -516        129   66      -4    2e-04 ***
## day                                   30         12   15       2     0.02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Lu
## ecsystm_tLu -0.197       
## day         -0.940  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Large connected to large"

## [1] "Large unconnected"

\(M_{M}\) vs \(M\)

ecosystem_type_i = c("Medium unconnected",
                     "Medium connected to medium")

Shannon

response_variable = "shannon"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.7   0.193     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     52.7     72.7    -18.3     36.7       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.25  -0.63  -0.08   0.87   2.60 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-02    0.167         
##             day         6e-05    0.008    -1.00
##  Residual               8e-02    0.291         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             1.418      0.118 15.033    12.0
## ecosystem_typeMedium unconnected       -0.214      0.205 15.033    -1.0
## day                                    -0.003      0.006 17.919    -0.5
## ecosystem_typeMedium unconnected:day    0.005      0.010 17.919     0.5
##                                      Pr(>|t|)    
## (Intercept)                             4e-09 ***
## ecosystem_typeMedium unconnected          0.3    
## day                                       0.7    
## ecosystem_typeMedium unconnected:day      0.6    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu day   
## ecsystm_tMu -0.577              
## day         -0.946  0.546       
## ecsystm_Mu:  0.546 -0.946 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1       -1   0.081   * weak
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##     50.9     68.4    -18.5     36.9       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.21  -0.61  -0.05   0.84   2.58 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-02    0.172         
##             day         7e-05    0.008    -1.00
##  Residual               8e-02    0.291         
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                         1.386      0.100 16.344    13.9    2e-10
## ecosystem_typeMedium unconnected   -0.118      0.066 60.800    -1.8     0.08
## day                                -0.001      0.005 17.656    -0.2     0.84
##                                     
## (Intercept)                      ***
## ecosystem_typeMedium unconnected .  
## day                                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu
## ecsystm_tMu -0.221       
## day         -0.924  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Biomass

response_variable = "bioarea_mm2_per_ml"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1     -1.6   0.062   * weak
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    217.6    237.6   -100.8    201.6       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -1.84  -0.75  -0.03   0.61   2.69 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 3e-01    0.59          
##             day         4e-04    0.02     -1.00
##  Residual               5e-01    0.70          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                      Estimate Std. Error    df t value Pr(>|t|)
## (Intercept)                              5.68       0.32 18.95      18    2e-13
## ecosystem_typeMedium unconnected        -1.37       0.55 18.95      -2     0.02
## day                                     -0.19       0.01 29.46     -13    1e-13
## ecosystem_typeMedium unconnected:day     0.05       0.03 29.46       2     0.04
##                                         
## (Intercept)                          ***
## ecosystem_typeMedium unconnected     *  
## day                                  ***
## ecosystem_typeMedium unconnected:day *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu day   
## ecsystm_tMu -0.577              
## day         -0.934  0.539       
## ecsystm_Mu:  0.539 -0.934 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.6   0.231     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    219.8    237.3   -102.9    205.8       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -1.77  -0.76   0.01   0.48   2.73 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 5e-01    0.73          
##             day         7e-04    0.03     -1.00
##  Residual               5e-01    0.71          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                          5.31       0.29 16.44      18    2e-12 ***
## ecosystem_typeMedium unconnected    -0.27       0.19 23.37      -1      0.2    
## day                                 -0.17       0.01 20.93     -13    1e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu
## ecsystm_tMu -0.224       
## day         -0.922  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Richness

response_variable = "species_richness"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      2.5   0.479     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    322.5    342.5   -153.2    306.5       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.68  -0.66   0.07   0.67   2.21 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1.146    1.07          
##             day         0.002    0.05     -0.98
##  Residual               1.601    1.27          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             7.711      0.572 15.000    13.5
## ecosystem_typeMedium unconnected       -0.216      0.990 15.000    -0.2
## day                                    -0.098      0.028 15.000    -3.5
## ecosystem_typeMedium unconnected:day   -0.009      0.049 15.000    -0.2
##                                      Pr(>|t|)    
## (Intercept)                             9e-10 ***
## ecosystem_typeMedium unconnected        0.830    
## day                                     0.003 ** 
## ecosystem_typeMedium unconnected:day    0.852    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu day   
## ecsystm_tMu -0.577              
## day         -0.946  0.546       
## ecsystm_Mu:  0.546 -0.946 -0.577
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.6   0.231     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##    320.5    338.0   -153.3    306.5       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.68  -0.65   0.09   0.67   2.22 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1.153    1.07          
##             day         0.002    0.05     -0.98
##  Residual               1.601    1.27          
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error    df t value Pr(>|t|)    
## (Intercept)                          7.77       0.48 16.38      16    2e-11 ***
## ecosystem_typeMedium unconnected    -0.39       0.32 15.00      -1      0.2    
## day                                 -0.10       0.02 15.00      -4    5e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu
## ecsystm_tMu -0.223       
## day         -0.922  0.000
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Evenness

response_variable = "evenness_pielou"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      0.1   0.144     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -130.3   -110.3     73.1   -146.3       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##  -2.30  -0.67   0.06   0.66   2.10 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         4e-17    6e-09     NaN
##  Residual               1e-02    1e-01        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             0.682      0.039 90.000      18
## ecosystem_typeMedium unconnected       -0.134      0.068 90.000      -2
## day                                     0.005      0.002 90.000       3
## ecosystem_typeMedium unconnected:day    0.006      0.004 90.000       2
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeMedium unconnected        0.050 *  
## day                                     0.009 ** 
## ecosystem_typeMedium unconnected:day    0.070 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu day   
## ecsystm_tMu -0.577              
## day         -0.935  0.540       
## ecsystm_Mu:  0.540 -0.935 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.4   0.446     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   -129.0   -111.5     71.5   -143.0       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.4   -0.7    0.1    0.7    2.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr
##  culture_ID (Intercept) 0e+00    0e+00        
##             day         2e-17    4e-09     NaN
##  Residual               1e-02    1e-01        
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error     df t value Pr(>|t|)
## (Intercept)                         0.643      0.033 90.000    19.2   <2e-16
## ecosystem_typeMedium unconnected   -0.019      0.024 90.000    -0.8      0.4
## day                                 0.008      0.002 90.000     4.5    2e-05
##                                     
## (Intercept)                      ***
## ecosystem_typeMedium unconnected    
## day                              ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu
## ecsystm_tMu -0.243       
## day         -0.907  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Median Size

response_variable = "median_body_area_µm2"

We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:

plot.ecosystems.points(ds_ecosystems,
                    ecosystem_type_i,
                    response_variable)

 

Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.

filtered_data = ds_ecosystems %>%
  filter(time_point >= first_time_point_model,
         time_point <= last_time_point_model,
         ecosystem_type %in% ecosystem_type_i,
         !is.na(!!sym(response_variable)))
plot.ecosystems.points(filtered_data,
                    ecosystem_type_i,
                    response_variable) 

 

Then, given that we have gathered measurements from the same ecosystem on multiple occasions, we can develop mixed effect models to examine how the connection influenced this variable. To study the effects of ecosystem connection we compare two models to a null model using ANOVA: a full model and a reduced model. In all models, we treat culture ID as having a random effect on how the slope and intercept of the relationship between response variable and time, with the slope and intercept being correlated (Bates et al. 2015). The full model contains the interaction of connection with time (Response variable ~ connection * day + (day | culture ID)), the reduced model contains the connection but without the interaction with time (Response variable ~ connection + day + (day | culture ID)), and the null model doesn’t contain the connection at all (Response variable ~ day + (day | culture ID)). If any of the two model comparisons is significant, then ecosystem connection had an effect.

full_model = lmer(
  get(response_variable) ~
    ecosystem_type * day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

reduced_model = lmer(
  get(response_variable) ~
    ecosystem_type + day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))

null_model = lmer(
  get(response_variable) ~
    day +
    (day | culture_ID),
  data = filtered_data,
  REML = FALSE,
  control = lmerControl(optimizer = "Nelder_Mead"))


Full model vs null model

Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
                                       null_model,
                                       "mixed_model") 

model_stats_full %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      3.7   0.862     none
Click to view the full model output
print(summary(full_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1446.3   1466.3   -715.2   1430.3       82 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.4    0.1    0.5    3.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e+05    782           
##             day         3e+03     54      -1.00
##  Residual               4e+05    611           
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                      Estimate Std. Error   df t value Pr(>|t|)
## (Intercept)                              3405        332   16    10.2    2e-08
## ecosystem_typeMedium unconnected          -89        576   16    -0.2      0.9
## day                                        14         21   15     0.7      0.5
## ecosystem_typeMedium unconnected:day       10         36   15     0.3      0.8
##                                         
## (Intercept)                          ***
## ecosystem_typeMedium unconnected        
## day                                     
## ecosystem_typeMedium unconnected:day    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu day   
## ecsystm_tMu -0.577              
## day         -0.966  0.558       
## ecsystm_Mu:  0.558 -0.966 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the full model residual plots
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(full_model),
           residuals = resid(full_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(full_model))


Reduced vs null model

Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
                                          null_model,
                                          "mixed_model") 

model_stats_reduced %>%
  mutate(deltaAIC = round(deltaAIC, digits = 1),
         p_value = round(p_value, digits = 3),
         R2 = NULL,
         evidence = "",
         evidence = ifelse(p_value > 0.1, 
                           "none",
                           evidence),
         evidence = ifelse(p_value < 0.1, 
                           "* weak",
                           evidence),
         evidence = ifelse(p_value < 0.05, 
                           "** moderate",
                           evidence),
         evidence = ifelse(p_value < 0.01, 
                           "*** strong",
                           evidence),
         evidence = ifelse(p_value < 0.001, 
                           "**** very strong",
                           evidence),
         p_value = ifelse(p_value < 0.001,
                           "< 0.001",
                           p_value)) %>%
  print()
##   deltaAIC p_value evidence
## 1      1.8   0.642     none
Click to view the reduced model output
print(summary(reduced_model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
##    Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
## 
##      AIC      BIC   logLik deviance df.resid 
##   1444.4   1461.9   -715.2   1430.4       83 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -2.6   -0.5    0.1    0.5    3.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e+05    785           
##             day         3e+03     55      -1.00
##  Residual               4e+05    611           
## Number of obs: 90, groups:  culture_ID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error   df t value Pr(>|t|)    
## (Intercept)                          3352        277   17    12.1    8e-10 ***
## ecosystem_typeMedium unconnected       70        149   49     0.5      0.6    
## day                                    17         17   15     1.0      0.3    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) ecs_Mu
## ecsystm_tMu -0.180       
## day         -0.950  0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
    mutate(predicted = fitted(reduced_model),
           residuals = resid(reduced_model)) %>%
    plot_ly(x = ~predicted,
            y = ~residuals,
            type = "scatter",
            mode = "markers",
            marker = list(size = 5, color = "#4C78A8"),
            text = paste(" ID: ", 
                         filtered_data$culture_ID, 
                         "<br>",
                         "Day: ", 
                         filtered_data$day, 
                         "<br>",
                         "Patch Type: ", 
                         filtered_data$ecosystem_type, 
                         "<br>",
                         "Biomass density: ", 
                         round(filtered_data$bioarea_mm2_per_ml, digits = 2), 
                         "<br>",
                         "Species richness: ", 
                         filtered_data$species_richness, 
                         "<br>"),
            hoverinfo = "text") %>%
    plotly::layout(title = "Residuals vs. Fitted Values",
                   xaxis = list(title = "Fitted Values"),
                   yaxis = list(title = "Residuals"))
res_vs_fit
qqnorm(resid(reduced_model))

Populations

for(ecosystem_type_i in ecosystem_type_i){
  
  print(ecosystem_type_i)

  p = ds_ecosystems %>%
  filter(ecosystem_type == ecosystem_type_i) %>%
  group_by(day) %>%
  summarise(
    Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
    # Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
    # Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
    Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
    Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
    Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
    Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
    Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
    Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
    Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
    Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
    Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
    Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
  ) %>%
  pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
  ggplot(aes(
    x = day,
    y = species_indiv_per_ml,
    group = interaction(day, species),
    color = species
  )) +
  geom_point(position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_line(
    aes(group = species),
    position = position_dodge(dodging),
    linewidth = treatment_lines_linewidth) + 
  labs(x = axis_names %>% 
         filter(variable == "day") %>% 
         pull(axis_name),
       y = axis_names %>% 
         filter(variable == "dominance") %>% 
         pull(axis_name)) +
  coord_cartesian(ylim = c(0, 100))
  
  print(p)

}
## [1] "Medium unconnected"

## [1] "Medium connected to medium"

Results

Meta-ecosystem diversity & function

We want here to plot the final paper version of the biodiversity and productivity of meta-ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to change the size of the plot.

# Define meta-ecosystems you want to plot.

metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
                         "Medium-Medium unconnected",
                         "Small-Large meta-ecosystem",
                         "Small-Large unconnected")
# Write function to plot a response variable. Afterwards you can use this function to plot alpha, beta, gamma diversity, and biomass.

plot.single.plot = function(response_variable){
  
  ds_metaecosystems %>%
    filter(metaecosystem_type %in% metaecosystem_type_i,
           !is.na(!!sym(response_variable))) %>%
    summarySE(measurevar = response_variable,
              groupvars = c("day", "metaecosystem_type", "type", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable),
               group = interaction(day, metaecosystem_type),
               color = type,
               linetype = connection)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = metaecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable) + ci,
                      ymin = get(response_variable) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable],
         color = "") +
    scale_color_manual(values = c("#762a83",
                                  "#1b7837")) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 2),
           linetype = guide_legend(title = NULL,
                                   nrow = 2)) +
    theme(plot.margin = unit(c(ggarrange_margin_left,
                               ggarrange_margin_right,
                               ggarrange_margin_bottom,
                               ggarrange_margin_left),
                             "cm")) +
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# Combine plots of alpha, beta, gamma biodiversity and biomass.

p_combined = ggarrange(plot.single.plot("mean_shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", size = paper_labels_size) +
                         font("ylab", size = paper_labels_size),
                       plot.single.plot("bray_curtis") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("metaecosystem_richness") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("total_metaecosystem_bioarea_mm2") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(ds_metaecosystems$day)),
                       heights = c(0.8, 0.8, 0.8, 1),
                       nrow = 4,
                       common.legend = TRUE,
                       align = "v",
                       labels = c("(a)", "(b)", "(c)", "(d)"),
                       label.x = 0.1,
                       label.y = 0.8) %>%
  print()

Ecosystem diversity & function

We want here to plot the final paper version of the biodiversity and productivity of the small and large ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.

# Define ecosystems you want to plot.

ecosystem_type_input = c("Small connected to large",
                     "Small connected to small",
                     "Small unconnected",
                     "Large connected to small",
                     "Large connected to large",
                     "Large unconnected")
# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.

plot.single.plot = function(response_variable){
  
  ds_ecosystems %>%
    filter(ecosystem_type %in% ecosystem_type_input,
           !is.na(!!sym(response_variable))) %>%
    summarySE(measurevar = response_variable,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable) + ci,
                      ymin = get(response_variable) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable],
         color = "") +
    scale_color_manual(values = c("#993404",
                                  "#993404",
                                  "#993404",
                                  "#3182bd",
                                  "#3182bd",
                                  "#3182bd"),
                       label = expression(S[L], 
                                          S[S],
                                          S,
                                          L[S], 
                                          L[L], 
                                          L)) +
    scale_linetype_manual(values = c("solid",
                                     "dashed",
                                     "dotted",
                                     "solid",
                                     "dashed",
                                     "dotted"),
                          label = expression(S[L], 
                                             S[S],
                                             S,
                                             L[S], 
                                             L[L], 
                                             L)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# Combine plots

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(ds_ecosystems$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

We want here to plot the final paper version of the biodiversity and productivity of the medium ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.

# Define ecosystems you want to plot.

ecosystem_type_input = c("Medium connected to medium",
                     "Medium unconnected")
# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.

plot.single.plot = function(response_variable){
  
  ds_ecosystems %>%
    filter(ecosystem_type %in% ecosystem_type_input,
           !is.na(!!sym(response_variable))) %>%
    summarySE(measurevar = response_variable,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable) + ci,
                      ymin = get(response_variable) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable],
         color = "") +
    scale_color_manual(values = c("#d95f0e",
                                  "#d95f0e"),
                       label = expression(M[M], 
                                          M)) +
    scale_linetype_manual(values = c("dashed",
                                     "dotted"),
                          label = expression(M[M], 
                                             M)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# Combine plots

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(ds_ecosystems$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()

Ecosystem autotrophic/heterotrophic ratio

We want here to plot the final paper version of the ratio between autotrophic and heterotrophic biomass in small, medium, and large unconnected ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have S, M, and L in the legend.

# Define ecosystems and response variable you want to plot.

ecosystem_type_input = c("S",
                     "M",
                     "L")

response_variable = "auto_hetero_ratio"
# Construct plot

p = ds_ecosystems %>%
  
  # Manipulate
  
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                ecosystem_type == "Medium unconnected" ~ "M",
                                ecosystem_type == "Large unconnected" ~ "L")) %>%
  filter(ecosystem_type %in% ecosystem_type_input,
         !is.na(!!sym(response_variable))) %>%
  summarySE(measurevar = response_variable,
            groupvars = c("day", "ecosystem_type", "ecosystem_size", "connection")) %>%
  
  # Create plot
  
  ggplot(aes(x = day,
             y = get(response_variable),
             group = interaction(day, ecosystem_type),
             color = ecosystem_type)) +
  
  # Points
  
  geom_point(stat = "summary",
             fun = "mean",
             position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_errorbar(aes(ymax = get(response_variable) + ci,
                    ymin = get(response_variable) - ci),
                width = width_errorbar,
                position = position_dodge(dodging)) +
  
  # Lines
  
  geom_line(stat = "summary",
            fun = "mean",
            aes(group = ecosystem_type),
            position = position_dodge(dodging),
            linewidth = treatment_lines_linewidth) +
  
  # Axes and legend
  
  labs(x = axis_names$axis_name[axis_names$variable == "day"],
       y = axis_names$axis_name[axis_names$variable == response_variable],
       color = "") +
  scale_x_continuous(breaks = unique(ds_ecosystems$day)) +
  guides(color = guide_legend(title = NULL,
                              nrow = 1),
         linetype = guide_legend(title = NULL,
                                 nrow = 1)) +
  scale_color_manual(values = c("#000000",
                                "#737373",
                                "#bdbdbd")) +
  
  # Extra graphic elements
  
  theme_bw() +
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        legend.position = legend_position,
        legend.key.width = unit(legend_width_cm, "cm"),
        axis.title.x = element_text(size = paper_labels_size),
        axis.title.y = element_text(size = paper_labels_size),
        legend.text = element_text(size = paper_labels_size)) +
  geom_rect(xmin = grey_background_xmin, 
            xmax = grey_background_xmax,
            ymin = grey_background_ymin, 
            ymax = grey_background_ymax, 
            fill = grey_background_fill, 
            alpha = grey_background_alpha,
            color = grey_background_color) + 
  geom_hline(yintercept = 0,
             color = zero_line_colour,
             linetype = zero_line_line_type,
             linewidth = zero_line_line_width) +
  
  geom_vline(xintercept = resource_flow_days,
             linetype = resource_flow_line_type,
             color = resource_flow_line_colour,
             linewidth = resource_flow_line_width)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p

Evaporation

During the experiment we noticed that microwaving ecosystem sub-samples for three minutes to create disturbance caused the evaporation of the ecosystems. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of 5.75 and 6.75 ml of deionised water, which represent low and high disturbance, respectively. For each disturbance level, I microwaved 15 tubes of that disturbance level for three minutes and measured their evaporation. To do so, I weighed the water before the microwaving (weigh tubes, add water, reweigh tubes) and after it (weigh Becker, pour water into it, reweigh Becker).

evaporation.test = read.csv(here("1_experiment", "evaporation_test","evaporation_test_initial.csv"), header = TRUE)

evaporation.test %>%
  ggplot(aes (x = as.character(water_pipetted),
                y = weight_water_evaporated,
                group = interaction(water_pipetted, as.character(rack)),
                fill = as.character(rack))) +
  geom_boxplot(width = boxplot_width) +
  labs(x = "Water volume (ml)" , 
       y = "Evaporation (g)", 
       fill = "Rack replicate")

Furthermore, during the experiment we noticed that microwaving five 6.75 ml ecosystems sub-samples with ten empty tubes for three minutes to create disturbance caused the evaporation of the sub-samples more than if they were with other sub-samples. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of five 6.75 ml sub-samples with ten empty or filled falcon tubes. The weighting was conducted as above.

evaporation.test = read.csv(here("1_experiment", "evaporation_test", "evaporation_test_fill_nofill.csv"), header = TRUE)

evaporation.test %>%
  ggplot(aes (x = all_tubes_water,
              y = weight_water_evaporated)) +
  geom_boxplot(width = boxplot_width) +
  labs(x = "Water in the other 10 tubes" , 
  y = "Evaporation (g)")

Analysis scripts

Video analysis

To analyse the videos I took of the ecosystems, I used the package BEMOVI. For this, I had to use the powerful computer. Below is the code utilised for video analysis on the powerful computer.

# Clear workspace
rm(list = ls())

# Set working directory
setwd("/media/mendel-himself/ID_061_Ema2/PatchSizePilot/training")

# Load required libraries
# library(devtools)
# install_github("femoerman/bemovi", ref="master")
library(bemovi)
library(parallel)
library(doParallel)
library(foreach)

# Define memory allocation parameters (in MB)
memory.alloc <- 240000           # Total memory allocated
memory.per.identifier <- 40000   # Memory per identifier
memory.per.linker <- 5000        # Memory per linker
memory.per.overlay <- 60000      # Memory per overlay

# Set paths for tools and particle linker
tools.path <- "/home/mendel-himself/bemovi_tools/" # Path to tools folder
to.particlelinker <- tools.path

# Set directories and file names
to.data <- paste(getwd(), "/", sep = "")
video.description.folder <- "0_video_description/"
video.description.file <- "video_description.txt"
raw.video.folder <- "1_raw/"
raw.avi.folder <- "1a_raw_avi/"
metadata.folder <- "1b_raw_meta/"
particle.data.folder <- "2_particle_data/"
trajectory.data.folder <- "3_trajectory_data/"
temp.overlay.folder <- "4a_temp_overlays/"
overlay.folder <- "4_overlays/"
merged.data.folder <- "5_merged_data/"
ijmacs.folder <- "ijmacs/"

######################################################################
# VIDEO PARAMETERS

# Define video parameters
fps <- 25                  # Video frame rate (frames per second)
total_frames <- 125        # Total length of video (frames)
width <- 2048              # Video width (pixels)
height <- 2048             # Video height (pixels)
measured_volume <- 34.4    # Measured volume (microliters) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
pixel_to_scale <- 4.05     # Size of a pixel (micrometers) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
video.format <- "cxd"      # Video file format (avi, cxd, mov, tiff)
difference.lag <- 10       # Difference lag
thresholds <- c(13, 255)   # Threshold values of pixel intensity (considered a measure of pixel "whiteness") for determining if a pixel belongs to an individual rather than the background

######################################################################
# FILTERING PARAMETERS
# optimized for Perfex Pro 10 stereomicrocope with Perfex SC38800 (IDS UI-3880LE-M-GL) camera
# tested stereomicroscopes: Perfex Pro 10, Nikon SMZ1500, Leica M205 C
# tested cameras: Perfex SC38800, Canon 5D Mark III, Hamamatsu Orca Flash 4
# tested species: Tet, Col, Pau, Pca, Eug, Chi, Ble, Ceph, Lox, Spi

particle_min_size <- 10           # Minimum particle size (pixels)
particle_max_size <- 1000         # Maximum particle size (pixels)
trajectory_link_range <- 3        # Number of adjacent frames for linking particles
trajectory_displacement <- 16     # Maximum displacement of a particle between frames

# Filtering criteria
filter_min_net_disp <- 25         # Minimum net displacement (µm)
filter_min_duration <- 1          # Minimum duration (s)
filter_detection_freq <- 0.1      # Minimum detection frequency (1/s)
filter_median_step_length <- 3    # Minimum median step length (µm)

######################################################################
# VIDEO ANALYSIS

# Check if all tools are installed and set permissions
check_tools_folder(tools.path)
system(paste0("chmod a+x ", tools.path, "bftools/bf.sh"))
system(paste0("chmod a+x ", tools.path, "bftools/bfconvert"))
system(paste0("chmod a+x ", tools.path, "bftools/showinf"))

# Convert video files to compressed avi format
convert_to_avi(to.data,
               raw.video.folder,
               raw.avi.folder,
               metadata.folder,
               tools.path,
               fps,
               video.format)


# Uncomment the following lines for testing
# check_video_file_names(to.data, raw.avi.folder, video.description.folder, video.description.file)
# check_threshold_values(to.data, raw.avi.folder, ijmacs.folder, 2, difference.lag, thresholds, tools.path, memory.alloc)

# Identify particles in the video
locate_and_measure_particles(to.data,
                             raw.avi.folder,
                             particle.data.folder,
                             difference.lag,
                             min_size = particle_min_size,
                             max_size = particle_max_size,
                             thresholds = thresholds,
                             tools.path,
                             memory = memory.alloc,
                             memory.per.identifier = memory.per.identifier,
                             max.cores = detectCores() - 1)

# Link particles across frames to form trajectories
link_particles(to.data,
               particle.data.folder,
               trajectory.data.folder,
               linkrange = trajectory_link_range,
               disp = trajectory_displacement,
               start_vid = 1,
               memory = memory.alloc,
               memory_per_linkerProcess = memory.per.linker,
               raw.avi.folder,
               max.cores = detectCores() - 1,
               max_time = 1)

# Merge video description file with particle data
merge_data(to.data,
           particle.data.folder,
           trajectory.data.folder,
           video.description.folder,
           video.description.file,
           merged.data.folder)

# Load the merged data
load(paste0(to.data, merged.data.folder, "Master.RData"))

# Filter trajectory data based on defined criteria
trajectory.data.filtered <- filter_data(trajectory.data,
                                        filter_min_net_disp,
                                        filter_min_duration,
                                        filter_detection_freq,
                                        filter_median_step_length)

# Summarize trajectory data to individual-based data
morph_mvt <- summarize_trajectories(trajectory.data.filtered,
                                    calculate.median = F,
                                    write = T,
                                    to.data,
                                    merged.data.folder)

# Summarize sample level data
summarize_populations(trajectory.data.filtered,
                      morph_mvt,
                      write = T,
                      to.data,
                      merged.data.folder,
                      video.description.folder,
                      video.description.file,
                      total_frames)

# Create overlays for validation
create.subtitle.overlays(to.data,
                         traj.data = trajectory.data.filtered,
                         raw.video.folder,
                         raw.avi.folder,
                         temp.overlay.folder,
                         overlay.folder,
                         fps,
                         vid.length = total_frames / fps,
                         width,
                         height,
                         tools.path = tools.path,
                         overlay.type = "number",
                         video.format)

# Create overlays (old method)
create_overlays(traj.data = trajectory.data.filtered,
                to.data = to.data,
                merged.data.folder = merged.data.folder,
                raw.video.folder = raw.avi.folder,
                temp.overlay.folder = "4a_temp_overlays_old/",
                overlay.folder = "4_overlays_old/",
                width = width,
                height = height,
                difference.lag = difference.lag,
                type = "traj",
                predict_spec = F,
                contrast.enhancement = 1,
                IJ.path = "/home/mendel-himself/bemovi_tools",
                memory = memory.alloc,
                max.cores = detectCores() - 1,
                memory.per.overlay = memory.per.overlay)

Species identification

To avoid transferring all the data from the powerful computer, I performed species identification on that system and subsequently imported the results into the Rstudio folder on my personal computer. Below is the code utilised for species identification on the powerful computer.

# Clear the workspace
rm(list = ls())

# Uncomment and install required packages if not already installed
#install.packages("e1071",dependencies = T)
#install.packages("devtools",dependencies = T)
#install_github("pennekampster/bemovi", ref="master")
#library(devtools)

# Load required libraries
library(bemovi)
library(e1071)
library("here")
library("tidyverse")

# Define time points in the experiment
time_points_in_experiment = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")

# Loop through each time point in the experiment
for (time_point in time_points_in_experiment) {
  
  # Define folder names and paths
  video.description.folder = "0_video_description/"
  video.description.file = "video_description.txt"
  merged.data.folder = "5_merged_data/"
  monocultures_folder_path = here("biomass_analysis", "training", "")
  mixed_cultures_folder_path = here("biomass_analysis", time_point, "")
  
  #Parameters used in the video analysis script
  fps = 25
  nsv = 5
  measured_volume = 34.4
  pixel_to_scale = 4.05
  filter_min_net_disp = 25
  filter_min_duration = 1
  filter_detection_freq = 0.1
  filter_median_step_length = 3
  
  # Load master dataset of mono-cultures
  load(paste0(monocultures_folder_path, merged.data.folder, "Master.RData"))
  trajectory.data_monocultures = trajectory.data
  rm(trajectory.data)
  
  # Filter the master data of mono-cultures using the same parameters as in the video analysis script
  trajectory.data_monocultures.filtered = filter_data(trajectory.data_monocultures,
                                                      filter_min_net_disp,
                                                      filter_min_duration,
                                                      filter_detection_freq,
                                                      filter_median_step_length)
  
  # Summarize trajectory data to individual-based data
  morph_mvt = summarize_trajectories(data = trajectory.data_monocultures.filtered,
                                     calculate.median = FALSE,
                                     write = TRUE,
                                     to.data = monocultures_folder_path,
                                     merged.data.folder = merged.data.folder) %>%
    mutate(comment = NULL)
  
  # Prepare training data by removing incomplete cases
  training_data = morph_mvt[complete.cases(morph_mvt), ]
  
  # Train SVM model on the training data
  svm1 = svm(
    factor(species) ~
      mean_grey +
      sd_grey +
      mean_area +
      sd_area +
      mean_perimeter +
      mean_turning +
      sd_turning +
      sd_perimeter +
      mean_major +
      sd_major +
      mean_minor +
      sd_minor +
      mean_ar +
      sd_ar +
      duration +
      max_net  +
      net_disp +
      net_speed +
      gross_disp +
      max_step +
      min_step +
      sd_step +
      sd_gross_speed +
      max_gross_speed +
      min_gross_speed ,
    data = training_data,
    probability = T,
    na.action = na.pass)
  
  # Generate and print confusion matrix
  confusion.matrix = table(svm1$fitted, training_data$species)
  confusion.matrix.nd = confusion.matrix
  diag(confusion.matrix.nd) = 0
  svm1$confusion = cbind(confusion.matrix,
                         class.error = rowSums(confusion.matrix.nd) / rowSums(confusion.matrix))
  
  print(paste("Confusion matrix of time point", time_point))
  print(svm1$confusion)
  
  # Extract unique species names
  species.names = unique(trajectory.data_monocultures$species)
  
  # Load mixed cultures dataset
  load(paste0(mixed_cultures_folder_path, merged.data.folder, "Master.RData"))
  trajectory.data_mixed = trajectory.data
  rm(trajectory.data)
  
  # Filter mixed cultures data using the same parameters
  trajectory.data_mixed.filtered = filter_data(trajectory.data_mixed,
                                               filter_min_net_disp,
                                               filter_min_duration,
                                               filter_detection_freq,
                                               filter_median_step_length)
  
  # Summarize trajectory data to individual-based data
  morph_mvt = summarize_trajectories(data = trajectory.data_mixed.filtered,
                                     calculate.median = FALSE,
                                     write = TRUE,
                                     to.data = mixed_cultures_folder_path,
                                     merged.data.folder = merged.data.folder)[, which(colnames(morph_mvt) != "Col_manual")] %>%
    mutate(comment = NULL)
  
  # Prepare data for prediction by removing incomplete cases
  data.to.predict = morph_mvt[complete.cases(morph_mvt),]
  
  # Predict species using the trained SVM model
  p.id = predict(object = svm1, data.to.predict, type = "response")
  data.to.predict$predicted_species = as.character(p.id)
  
  # Summarize population data
  pop.data = summarize_populations(traj.data = trajectory.data_monocultures.filtered,
                                   sum.data = morph_mvt,
                                   write = TRUE,
                                   to.data = mixed_cultures_folder_path,
                                   merged.data.folder = merged.data.folder,
                                   video.description.folder = video.description.folder,
                                   video.description.file = video.description.file,
                                   total_frame = fps * nsv)
  
  # Function to calculate species density
  species.density = function(sample_output,
                             indiv_predicted,
                             species_names,
                             total_frames,
                             mv = measured_volume) {
    samples = unique(indiv_predicted$file)
    
    sp.dens = matrix(0,
                     nrow(sample_output),
                     length(species_names))
    
    colnames(sp.dens) = species_names
    
    for (i in 1:length(samples)) {
      indiv = subset(indiv_predicted, file == samples[i])
      
      spec = unique(indiv$predicted_species)
      
      for (j in 1:length(spec)) {
        all.indiv.sp = subset(indiv,
                              predicted_species == spec[j])
        
        dens = sum(all.indiv.sp$N_frames) / total_frames / mv
        sp.dens[which(sample_output$file == as.character(samples[i])), which(species_names == spec[j])] = dens
      }
    }
    
    return(cbind(sample_output, sp.dens))
    
  }
  
  # Calculate species density for the current time point
  output = species.density(pop.data,
                           data.to.predict,
                           species.names,
                           total_frames = fps * nsv,
                           mv = measured_volume)
  
  # Save the species density results to a CSV file
  file_name = paste0("species_ID_", time_point, ".csv")
  write.csv(output, here("biomass_analysis", "species_ID_results", file_name))
  rm(output)
  
}

Other

Running time

## Time difference of 1.8 mins

Disturbance input

Check that disturbance_global_input is what you set:

print(paste0("Disturbance = ", disturbance_global_input))
## [1] "Disturbance = high"

Useful code

If you want to change a certain part of the code using the following code in Unix:

#Rmd script
cd /Users/Ema/Documents/Github/PatchSize/3_r_files
sed -i '' 's/old_string/new_string/g' *.Rmd

#R script
cd /Users/ema/Documents/GitHub/PatchSize/3_r_files/functions
sed -i '' 's/old_string/new_string/g' *.R

you want to share a dataset and get a reproducible object, use the following R code:

dput()

Crashed cultures

The only type of ecosystem where all cultures crashed was small connected to small at high disturbance.

R version

R.version.string
## [1] "R version 4.3.2 (2023-10-31)"

R package versions

The R packages we used with their version are as follows:

sessionInfo()
## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.2.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Europe/Zurich
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices datasets  utils     methods   base     
## 
## other attached packages:
##  [1] conflicted_1.2.0 combinat_0.0-8   Rmisc_1.5.1      betapart_1.6    
##  [5] vegan_2.6-6.1    lattice_0.22-6   permute_0.9-7    lmerTest_3.1-3  
##  [9] lme4_1.1-35.4    Matrix_1.6-5     plotly_4.10.4    ggpubr_0.6.0    
## [13] lubridate_1.9.3  forcats_1.0.0    stringr_1.5.1    dplyr_1.1.4     
## [17] purrr_1.0.2      readr_2.1.5      tidyr_1.3.1      tibble_3.2.1    
## [21] ggplot2_3.5.1    tidyverse_2.0.0  plyr_1.8.9       renv_1.0.7.9000 
## [25] testthat_3.2.1.1 here_1.0.1      
## 
## loaded via a namespace (and not attached):
##  [1] gridExtra_2.3       rlang_1.1.4         magrittr_2.0.3     
##  [4] compiler_4.3.2      mgcv_1.9-0          vctrs_0.6.5        
##  [7] pkgconfig_2.0.3     fastmap_1.2.0       backports_1.5.0    
## [10] labeling_0.4.3      magic_1.6-1         utf8_1.2.4         
## [13] rmarkdown_2.27      pracma_2.4.4        tzdb_0.4.0         
## [16] nloptr_2.1.1        itertools_0.1-3     waldo_0.5.2        
## [19] xfun_0.45           cachem_1.1.0        jsonlite_1.8.8     
## [22] highr_0.11          broom_1.0.6         parallel_4.3.2     
## [25] cluster_2.1.4       R6_2.5.1            bslib_0.7.0        
## [28] stringi_1.8.4       pkgload_1.3.4       car_3.1-2          
## [31] boot_1.3-30         brio_1.1.5          jquerylib_0.1.4    
## [34] rcdd_1.6            numDeriv_2016.8-1.1 Rcpp_1.0.12        
## [37] iterators_1.0.14    knitr_1.47          snow_0.4-4         
## [40] picante_1.8.2       splines_4.3.2       timechange_0.3.0   
## [43] tidyselect_1.2.1    rstudioapi_0.16.0   abind_1.4-5        
## [46] yaml_2.3.8          codetools_0.2-20    minpack.lm_1.2-4   
## [49] withr_3.0.0         evaluate_0.24.0     desc_1.4.3         
## [52] pillar_1.9.0        carData_3.0-5       foreach_1.5.2      
## [55] geometry_0.4.7      generics_0.1.3      rprojroot_2.0.4    
## [58] hms_1.1.3           munsell_0.5.1       scales_1.3.0       
## [61] minqa_1.2.7         glue_1.7.0          lazyeval_0.2.2     
## [64] tools_4.3.2         data.table_1.15.4   ggsignif_0.6.4     
## [67] cowplot_1.1.3       fastmatch_1.1-4     grid_4.3.2         
## [70] ape_5.8             crosstalk_1.2.1     colorspace_2.1-0   
## [73] nlme_3.1-163        cli_3.6.3           optimx_2023-10.21  
## [76] fansi_1.0.6         viridisLite_0.4.2   doSNOW_1.0.20      
## [79] gtable_0.3.5        rstatix_0.7.2       sass_0.4.9         
## [82] digest_0.6.36       farver_2.1.2        htmlwidgets_1.6.4  
## [85] memoise_2.0.1       htmltools_0.5.8.1   lifecycle_1.0.4    
## [88] httr_1.4.7          MASS_7.3-60

References

Bates, Douglas, Martin Mächler, Benjamin M. Bolker, and Steven C. Walker. 2015. “Fitting Linear Mixed-Effects Models Using Lme4.” Journal of Statistical Software 67. https://doi.org/10.18637/jss.v067.i01.